Two students independently attempt to solve a certain problem. The .pdf
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Two students independently attempt to solve a certain problem. The probability that A solves it is 1/10 and the probability that B solves it is 1/3. What is the probability that the problem will be solved? Solution Probability of A = 1/2 Probability of B = 1/2 Probability that A can solve the problem= 1/10 probability that B can solve the problem = 1/3 P(Problem will be solved)= (1/2)*(1/10)+(1/2)*(1/3) = 13/60 =0.2167.
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X2468P(X)0.020.120.80.06X2.pdf
x1
x2
0
1
2
0
0.1
0.4
0.1
1
0.2
0.2
0
a. find P(X1 + X2>1)
b.Find f1(X1)
x1
x2
0
1
2
0
0.1
0.4
0.1
1
0.2
0.2
0
Solution
a) .2 + .1 = 0.3
b)0.2 + 0.2 = 0.4.
x1x201200.10.40.110.20.20a. find P(X.pdf
x1-x2-2x3=-3
3x1-2x2-3x3=-5
2x1 +2x3
|x1| |___| |___|
|x2|=|___|+|___|s.
|x3| |___| |___|
Solution
whats the third equation??? 2x1+2x3??? what is it equal to 3rd equation i think u
left some part of it now the time limit is also over so please re post the question with corrected
equations thanks.
X1 and X2 are independent Bernoulli random variables, each with prop.pdf
x1 : ______________? // x2:______________?
Explain me how can I solve it please
Solution
take derivative :
y\' = [2 + sinx][-sin x] - [cosx][cosx]/[2 + sinx]2
y\' = [ -2 sinx - 1 ]/ [2 + sinx]2
y\' = 0
1 + 2 sinx = 0
sinx = -1/2
x = n + (-1)n (-/6) where -/6 is principal angle
x1 = + /6 is the smalles +ve value
x2 = 11/6 is the next smallest positive value.
x.Solution1. Analyse2. Marketing Intelligence3. Deve.pdf
x.
Solution
x*x = x if and only if x = e. If x*x = x, multiply both sides on the left by y, where y
is theinverse of x. Then y * (x*x) = y * x, i.e., (y * x) * x = y *x (by associativity), so that e * x =
e (substituting y * x = e).But e * x = x, by the definition of identity. Thus x = e. Conversely, if x
= e, then e * e = e, since e * x = x for any x inG..
x.Solution 1.Globel market 2.Appendix 3.Mark.pdf
x.Hm />
Solution
Infinity plus 3 is still infinity so we can neglect the3
We end up with square root of n - square root of n
which means it exists at 0
For the sixth one we let n approach infinity
Since the series ends at n^2 / n^3 that can be rewritten as1/n
Since all the real numbers square is less than infinity theywill all approach zero
Everything approaches zero so adding them up will equalzero
Since the series ends at n^2 / n^3 that can be rewritten as1/n
Since all the real numbers square is less than infinity theywill all approach zero
Everything approaches zero so adding them up will equalzero
I dont think the limit exists for the second one
as infinity is neither odd nor even
So it could approach 2 or 0 meaning it does not exist
as infinity is neither odd nor even
So it could approach 2 or 0 meaning it does not exist.
x is a random variable with a probability distribution that is unifo.pdf
x is a random variable with a probability distribution that is uniform within the interval (0,1) and
zero outside that interval. What is the probability distribution of y = lnx?
Solution
cdf for x is given below
F(X<=x)=x-0/1-0=x
F(lnX<=lnx)=lnx
F(Y<=y)=lnx
pdf=dF/dx=(1/x)*(dy/dx)=(1/x)*(1)=(1/x)
=ey.
X is a normally distributed random variable with a standard deviatio.pdf
X is a normally distributed random variable with a standard deviation of 3.50. Find the
mean of X if 12.71% of the area under the distribution curve lies to the right of 14.49.
Solution
P(X = 14.49) = 0.1271 P((X - µx)/3.5 = (14.49 - µx)/3.5) = 0.1271 P(Z = z) =
0.1271 z = 1.14 1.14 = (14.49 - µx)/3.5 µx = 10.5.
Typical surveys involves about 500 people to 2000 people.When author.pdf
Typical surveys involves about 500 people to 2000 people.When author Shere Hite wrote
Woman and Love: A Cultrual Revolution in Progress, she based conclusions on a relativly large
sample of 4500 replies that she recived after mailing 100,000 questionaries to various women\'s
groups. Are her conclusions likely to be valid in the sense that they can be applied to the general
population of all women? Why or why not?
Solution
No they can\'t be applied to the general population of women. Two problems: 1.
Using a sample from people who voluntary mail a questionnare back is likely to introduce bias
into your survey because you will only get people who feel strongly about the subject matter. 2.
Just mailing it to womens\' groups gets the \"joiners\", who are probably not representative of the
female population as a whole..
Recommended
X2468P(X)0.020.120.80.06X2.pdf
x1
x2
0
1
2
0
0.1
0.4
0.1
1
0.2
0.2
0
a. find P(X1 + X2>1)
b.Find f1(X1)
x1
x2
0
1
2
0
0.1
0.4
0.1
1
0.2
0.2
0
Solution
a) .2 + .1 = 0.3
b)0.2 + 0.2 = 0.4.
x1x201200.10.40.110.20.20a. find P(X.pdf
x1-x2-2x3=-3
3x1-2x2-3x3=-5
2x1 +2x3
|x1| |___| |___|
|x2|=|___|+|___|s.
|x3| |___| |___|
Solution
whats the third equation??? 2x1+2x3??? what is it equal to 3rd equation i think u
left some part of it now the time limit is also over so please re post the question with corrected
equations thanks.
X1 and X2 are independent Bernoulli random variables, each with prop.pdf
x1 : ______________? // x2:______________?
Explain me how can I solve it please
Solution
take derivative :
y\' = [2 + sinx][-sin x] - [cosx][cosx]/[2 + sinx]2
y\' = [ -2 sinx - 1 ]/ [2 + sinx]2
y\' = 0
1 + 2 sinx = 0
sinx = -1/2
x = n + (-1)n (-/6) where -/6 is principal angle
x1 = + /6 is the smalles +ve value
x2 = 11/6 is the next smallest positive value.
x.Solution1. Analyse2. Marketing Intelligence3. Deve.pdf
x.
Solution
x*x = x if and only if x = e. If x*x = x, multiply both sides on the left by y, where y
is theinverse of x. Then y * (x*x) = y * x, i.e., (y * x) * x = y *x (by associativity), so that e * x =
e (substituting y * x = e).But e * x = x, by the definition of identity. Thus x = e. Conversely, if x
= e, then e * e = e, since e * x = x for any x inG..
x.Solution 1.Globel market 2.Appendix 3.Mark.pdf
x.Hm />
Solution
Infinity plus 3 is still infinity so we can neglect the3
We end up with square root of n - square root of n
which means it exists at 0
For the sixth one we let n approach infinity
Since the series ends at n^2 / n^3 that can be rewritten as1/n
Since all the real numbers square is less than infinity theywill all approach zero
Everything approaches zero so adding them up will equalzero
Since the series ends at n^2 / n^3 that can be rewritten as1/n
Since all the real numbers square is less than infinity theywill all approach zero
Everything approaches zero so adding them up will equalzero
I dont think the limit exists for the second one
as infinity is neither odd nor even
So it could approach 2 or 0 meaning it does not exist
as infinity is neither odd nor even
So it could approach 2 or 0 meaning it does not exist.
x is a random variable with a probability distribution that is unifo.pdf
x is a random variable with a probability distribution that is uniform within the interval (0,1) and
zero outside that interval. What is the probability distribution of y = lnx?
Solution
cdf for x is given below
F(X<=x)=x-0/1-0=x
F(lnX<=lnx)=lnx
F(Y<=y)=lnx
pdf=dF/dx=(1/x)*(dy/dx)=(1/x)*(1)=(1/x)
=ey.
X is a normally distributed random variable with a standard deviatio.pdf
X is a normally distributed random variable with a standard deviation of 3.50. Find the
mean of X if 12.71% of the area under the distribution curve lies to the right of 14.49.
Solution
P(X = 14.49) = 0.1271 P((X - µx)/3.5 = (14.49 - µx)/3.5) = 0.1271 P(Z = z) =
0.1271 z = 1.14 1.14 = (14.49 - µx)/3.5 µx = 10.5.
Typical surveys involves about 500 people to 2000 people.When author.pdf
Typical surveys involves about 500 people to 2000 people.When author Shere Hite wrote
Woman and Love: A Cultrual Revolution in Progress, she based conclusions on a relativly large
sample of 4500 replies that she recived after mailing 100,000 questionaries to various women\'s
groups. Are her conclusions likely to be valid in the sense that they can be applied to the general
population of all women? Why or why not?
Solution
No they can\'t be applied to the general population of women. Two problems: 1.
Using a sample from people who voluntary mail a questionnare back is likely to introduce bias
into your survey because you will only get people who feel strongly about the subject matter. 2.
Just mailing it to womens\' groups gets the \"joiners\", who are probably not representative of the
female population as a whole..
Type your question hereIn a tabular format, construct a table that a.pdf
Type your question hereIn a tabular format, construct a table that answers the following
questions:
Solution
1.
2
4.
5. Morbidity refers to the state of being diseased or unhealthy. Mortality is the term used for the
number of people who died within a population.
two thousand frequent midwestern business travelers are asked which .pdf
two thousand frequent midwestern business travelers are asked which midwesterm they prefer:
indianapolis, sanit louis, chicago or milwaukee. the results were 100 liked indianapolis best, 450
liked saint louis, 1300 liked chicago, and the remainder preferred milwaukee. develop a
frequency table and a relative frequenncy table to summarize this information.
Solution
frequency table : indianapolis - 0.054 saintlouis - 0.2432 chicago - 0.7027 relative
frequency table: indianapolis -1 saintlouis -4.5 chicago -13.
Two students, Ryan Wattenberg and Emma Bennett, are discussing the i.pdf
Two students, Ryan Wattenberg and Emma Bennett, are discussing the idea of convergence over
coffee. Ryan considers convergence to be true in theory but impractical in the real world. He
claims that most low-income developing countries are stuck in a cycle of poverty and so cannot
catch up with developed countries. With increased globalization, Emma feels that the developing
countries are growing and will converge with higher-income countries eventually. Zoey Smith, a
friend of theirs, however thinks that the evidence on convergence is rather unclear. Despite the
fact that developing countries are growing much faster than the developed countries, she thinks
that they will not be able to catch up with the developed nations in the near future.
Which of the following, if true, would strengthen Ryan\'s argument that developing countries
will not catch up with developed countries?
a. Most developed countries do not have similar resources endowments.
b. Some of the fastest growing developing countries in the world also score well on many social
indicators.
c. Credit creation by the formal banking system in most developing countries has been falling or
stagnant in the last five years.
d. High population in developing countries, which for decades acted as a drag on growth, now
forms a productive workforce.
e. Most developed countries experienced a high degree of inequality in the initial phases of
economic growth.
Solution
Ans = D
The GDP growth rates of developing nations are on average more than those of developed
nations.During the period 1965-99 , the average annual growth rate was 4.1 percent for the low-
income nations, 4.2 percent for middle-income nations, and 3.2 percent for high-income nations .
Does this imply that the developing nations would soon converge with the developed?
Unfortunately, the growth patterns explained here do not imply that the world is on its path to
“convergence\". Much faster population growth in most of the developing nations offsets the
comparatively faster growth rates of GDP, leading to GDP per capita growth to be relatively
low or perhaps even negative.Thus, the gap between the average GNP per capita between
developing and developed nations has widened. During the past 40 years of the 20th century, the
gulf between the average income of the richest 20 nations and that of the poorest 20 has doubled
in size.
Sustained economic growth of the developing nations is an essential instrument for reducing
poverty and enhancing people’s standard of living. However, only economic growth is not
enough. In few nations poverty worsened in spite of the overall economic growth, due to
increased income inequality . This economic growth is socially unsustainable and causes social
conflict, and is harmful to further growth. Also, fast economic growth may lead to fast
environmental degradation, hampering the quality of life and thus decreasing economic
productivity..
Two students are working independently on a problem. Their respectiv.pdf
Two students are working independently on a problem. Their respective probabilities of solving
the problem are 1/3 and 3/4. What is the probability that at least one of them will solve the
problem?
Solution
probability of both of them solving the problem = 1/3 * 3/4 =3/12=1/4 probability
of atleast one of them solving the problem = 1/3 + 3/4 - 1/4 = 5/6.
Two sisters, Allison and Teri, have agreed to meet between 1 and 6 p.pdf
Two sisters, Allison and Teri, have agreed to meet between 1 and 6 pm at the Startalks coffee
shop on a particular day. In fact, Allison is equally likely to arrive at exactly 1 pm, 2 pm, 3 pm, 4
pm, 5 pm or 6 pm. Teri is also equally likely to arrive at each of these six times, and Allison
Solution
the answer is 1/6.
Two samples are selected from a population and a treatment is admini.pdf
Two samples are selected from a population and a treatment is administered to the samples. if
both samples have he same mean and the same variance, you are more likely to find a significant
treatment affected with a sample of n= 100 than with a sample of n=100 than with a sample of
n= 4
Solution
true.
Two researchers, Wiebe and Bortolotti, in 2002 examined the color in.pdf
Two researchers, Wiebe and Bortolotti, in 2002 examined the color in tail feathers of Northern
Flickers. It sometimes occurs that these birds have one tail feather, which differed from the rest
in terms of its color. This was perhaps because the feather had re-grown after having been lost.
The
Solution
1) 0.01
2) 0.58.
Two random variables X and Y have joint density for 0 x 1 and 0.pdf
Two random variables X and Y have joint density for 0 ? x ? 1 and 0 ? y ? 1, and f(x, y) = 0
otherwise.
Are X and Y independent?
Find Enter as a formula.
Find . Enter as a formula.
Solution
Are X and Y independent?
Yes, they are independent.
f_X(x) = (12/7) * (y + 2x)
f_Y(y) = (12/7) * (x).
Two persons are selected at random. Event A Their birthday is i.pdf
Two persons are selected at random.
Event A: Their birthday is in the fall.
Event B: Their birthday is in October.
The two events A and B are:
1. Not mutually exclusive
or
2. Mutually exclusive
Solution
Th events are not mutually exclusive since a birthday in october is also a birthday in
the Fall. Therefore answer is 1. Not mutually exclusive..
Two key sources of economic growth have been due to increases in res.pdf
Two key sources of economic growth have been due to increases in resources and
increases in productivity. What factors will contribute to falling U.S. GDP growth
rates into the future, and how would that impact you?
Solution
Increase in productivity and resources are the building block for any economy for that matter.
One of the prime reasons why US economy developed in the last century is because of the
importance given to trade and commerce as also industrialisation and optimum usage of
available resources. US had and still has abundance of metals and coal, the driving factors for
any industry. American economy is also one of the most open and most traded with economies
with every single nation being its trade partner. This is also understandable since nearly 40% of
capital used in US is imported. Then during 1940s and 1950s, there was a shift in labour class as
more and more people starting enrolling in higher education. Gradually, labour got more skilled
and productive.
Now, it is eactly the same factors that would result in a falling GDP and growth rate. Although
this would not really happen since the cycle of development is permanent and might take
generations to hit bottom rock, its several factors that would result in falling productivity to be
specific. Resources too should be counted for since their exhaustion can lead to some serious
economic disasters. Imagine what it might be if all coal reserves would suddenly vanish. You
will have each and every industry coming to a halt, there would be continuous electricity cuts,
productivity would go at zero levels and people\'s income would hit rock bottom. So definitely
resources play one of the most crucial parts when it comes to growth rates.
Take the case of productivity. Its the people who contribute towards productivity. The latter is
decided by education levels, population and taxation. Higher education simply leads to higher
levels of productivity. Economic history of US stands as an evidence. The higher the population,
lower is the productivity but only to certain limit. Since employment levels depend on
population, a scarcity in the latter cannot lead to higher growth. Similarly, too high population
leads to lower productivity and per capita income. Lastly is taxation, something that is still being
debated. too high tax levels act as deterrents to income growth, too low taxes inhibit economic
growth..
Two power generating units A and B operate in parallel to supply the.pdf
Two power generating units A and B operate in parallel to supply the power requirements of a
small city. The probability of failure of each unit is 0.1, where the probability that both fail is
0.02.
What is the probability that when there is a power failure only one of the two units will have
failed?
Solution
P(only one of them has failed) = P(Failure of A) + P(failure of B) - 2P(Failure of both)
= 0.1 + 0.1 - 2*0.02
= 0.16.
two frieends are to meet at the library. Each arrives at independent.pdf
two frieends are to meet at the library. Each arrives at independently and randomly selected
times wiithin afixed 1- hour period. Each agree to wait no more than 15 minutes for the other.
find the probability that the meet.
Solution
Let\'s take n = 2 variables ( the two people\' s arrivals ) ;
d = 60 min ( the entire period within they arrive) ;
t = 15/d = 15/60 = 0.25 ( fraction of entire period they wait );
The probability they meet is :
p = nt^(n-1) - (n-1)t^n = 2*0.25^1 - 1*0.25^2 = 0.4375.
Two fair dice are tossed. Let X denote the number appearing on the .pdf
Two fair dice are tossed. Let X denote the number appearing on the first die and Y the number
on the second. Show that X and Y are independent.
Solution
the number on 1st die does not effect the the probability of number on second die ...
Therfore the number appearing on 1st die and number on 2nd are independent events.
Two disks are independantly slected. What is the probability that n.pdf
Two disks are independantly slected. What is the probability that neither contains a missing
pulse if the poisson distribution parameter lamda=.2?
Solution
P(x=0) = e^-2 2^0/0! = e^-2
P(x=0) = e^-2 2^0 / 0! = e^-2
since both are independent !!
the probability that neither contains a missing pulse = e^-2 * e^-2 = 0.0183
thus ans.
Two independent discrete random variables X and Y have marginal dist.pdf
Two independent discrete random variables X and Y have marginal distributions
f1(x) = x/21 and f2(y) = y/36 for certain sets of values x and y. Find the bivariate distribution
f(x, y).
Solution
since the variables are independent, f(x,y)= f(x)* f(y) = x*y/(21*36) = xy/756.
Two friends board an airliner just before departure time. There are .pdf
Two friends board an airliner just before departure time. There are only ten seats left, two of
which are aisle seats. How many ways can the two people arrange themselves in available seats
so that at least one of them sits on the aisle?
Solution
total seats avaiable: 10
2= aisle , 8 = normal
1) both the friends get the aisle seats= 2P2= 2 ways
2) one gets an aisle seat while other gets the normal seat = 2P1x 8P1= 2x8 = 16 ways
Total way s= 2 + 16 = 18 ways.
Two international students were talking in the wake of the Singapore.pdf
Two international students were talking in the wake of the Singapore Air disaster a few years
ago. The first student said she had been intending to fly Singapore Air for the semester break,
but wasn
Solution
Poisson random variables are independent of time since last event..
Two people, both of whom are carriers for a recessive genetic disord.pdf
Two people, both of whom are carriers for a recessive genetic disorder (both are heterozygotes),
have a child. Given that the child is not affected by the disease, what is the probability that
he/she is a heterozygote (and thus carries the gene for the disorder)?
Solution
probability - 1/2.
Two people took turns tossing a fair die until one of them tossed a .pdf
Two people took turns tossing a fair die until one of them tossed a 6. Person A tossed first, B
second. A third, and so on. Given that perosn B threw the first 6, what is the probability that B
obtained the first 6 on her second toss (that is on, on the fourth toss overall)?
Solution
Geometric pmf -> x = n, p(1-p)^n P[6] = probability of rolling a 6 = 1/6 P[x = 4] =
(1/6)(5/6)^3 = 125/1296 = .09645.
Two measures of center for a distribution are 67.0 and 70.7. One of .pdf
Two measures of center for a distribution are 67.0 and 70.7. One of these is the mean and the
other is the median. Which is which? Explain your choice.
Solution
Need more information. If symmetrical Median = Mean. If skewed mean is in
direction of skewness..
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Type your question hereIn a tabular format, construct a table that a.pdf
Type your question hereIn a tabular format, construct a table that answers the following
questions:
Solution
1.
2
4.
5. Morbidity refers to the state of being diseased or unhealthy. Mortality is the term used for the
number of people who died within a population.
two thousand frequent midwestern business travelers are asked which .pdf
two thousand frequent midwestern business travelers are asked which midwesterm they prefer:
indianapolis, sanit louis, chicago or milwaukee. the results were 100 liked indianapolis best, 450
liked saint louis, 1300 liked chicago, and the remainder preferred milwaukee. develop a
frequency table and a relative frequenncy table to summarize this information.
Solution
frequency table : indianapolis - 0.054 saintlouis - 0.2432 chicago - 0.7027 relative
frequency table: indianapolis -1 saintlouis -4.5 chicago -13.
Two students, Ryan Wattenberg and Emma Bennett, are discussing the i.pdf
Two students, Ryan Wattenberg and Emma Bennett, are discussing the idea of convergence over
coffee. Ryan considers convergence to be true in theory but impractical in the real world. He
claims that most low-income developing countries are stuck in a cycle of poverty and so cannot
catch up with developed countries. With increased globalization, Emma feels that the developing
countries are growing and will converge with higher-income countries eventually. Zoey Smith, a
friend of theirs, however thinks that the evidence on convergence is rather unclear. Despite the
fact that developing countries are growing much faster than the developed countries, she thinks
that they will not be able to catch up with the developed nations in the near future.
Which of the following, if true, would strengthen Ryan\'s argument that developing countries
will not catch up with developed countries?
a. Most developed countries do not have similar resources endowments.
b. Some of the fastest growing developing countries in the world also score well on many social
indicators.
c. Credit creation by the formal banking system in most developing countries has been falling or
stagnant in the last five years.
d. High population in developing countries, which for decades acted as a drag on growth, now
forms a productive workforce.
e. Most developed countries experienced a high degree of inequality in the initial phases of
economic growth.
Solution
Ans = D
The GDP growth rates of developing nations are on average more than those of developed
nations.During the period 1965-99 , the average annual growth rate was 4.1 percent for the low-
income nations, 4.2 percent for middle-income nations, and 3.2 percent for high-income nations .
Does this imply that the developing nations would soon converge with the developed?
Unfortunately, the growth patterns explained here do not imply that the world is on its path to
“convergence\". Much faster population growth in most of the developing nations offsets the
comparatively faster growth rates of GDP, leading to GDP per capita growth to be relatively
low or perhaps even negative.Thus, the gap between the average GNP per capita between
developing and developed nations has widened. During the past 40 years of the 20th century, the
gulf between the average income of the richest 20 nations and that of the poorest 20 has doubled
in size.
Sustained economic growth of the developing nations is an essential instrument for reducing
poverty and enhancing people’s standard of living. However, only economic growth is not
enough. In few nations poverty worsened in spite of the overall economic growth, due to
increased income inequality . This economic growth is socially unsustainable and causes social
conflict, and is harmful to further growth. Also, fast economic growth may lead to fast
environmental degradation, hampering the quality of life and thus decreasing economic
productivity..
Two students are working independently on a problem. Their respectiv.pdf
Two students are working independently on a problem. Their respective probabilities of solving
the problem are 1/3 and 3/4. What is the probability that at least one of them will solve the
problem?
Solution
probability of both of them solving the problem = 1/3 * 3/4 =3/12=1/4 probability
of atleast one of them solving the problem = 1/3 + 3/4 - 1/4 = 5/6.
Two sisters, Allison and Teri, have agreed to meet between 1 and 6 p.pdf
Two sisters, Allison and Teri, have agreed to meet between 1 and 6 pm at the Startalks coffee
shop on a particular day. In fact, Allison is equally likely to arrive at exactly 1 pm, 2 pm, 3 pm, 4
pm, 5 pm or 6 pm. Teri is also equally likely to arrive at each of these six times, and Allison
Solution
the answer is 1/6.
Two samples are selected from a population and a treatment is admini.pdf
Two samples are selected from a population and a treatment is administered to the samples. if
both samples have he same mean and the same variance, you are more likely to find a significant
treatment affected with a sample of n= 100 than with a sample of n=100 than with a sample of
n= 4
Solution
true.
Two researchers, Wiebe and Bortolotti, in 2002 examined the color in.pdf
Two researchers, Wiebe and Bortolotti, in 2002 examined the color in tail feathers of Northern
Flickers. It sometimes occurs that these birds have one tail feather, which differed from the rest
in terms of its color. This was perhaps because the feather had re-grown after having been lost.
The
Solution
1) 0.01
2) 0.58.
Two random variables X and Y have joint density for 0 x 1 and 0.pdf
Two random variables X and Y have joint density for 0 ? x ? 1 and 0 ? y ? 1, and f(x, y) = 0
otherwise.
Are X and Y independent?
Find Enter as a formula.
Find . Enter as a formula.
Solution
Are X and Y independent?
Yes, they are independent.
f_X(x) = (12/7) * (y + 2x)
f_Y(y) = (12/7) * (x).
Two persons are selected at random. Event A Their birthday is i.pdf
Two persons are selected at random.
Event A: Their birthday is in the fall.
Event B: Their birthday is in October.
The two events A and B are:
1. Not mutually exclusive
or
2. Mutually exclusive
Solution
Th events are not mutually exclusive since a birthday in october is also a birthday in
the Fall. Therefore answer is 1. Not mutually exclusive..
Two key sources of economic growth have been due to increases in res.pdf
Two key sources of economic growth have been due to increases in resources and
increases in productivity. What factors will contribute to falling U.S. GDP growth
rates into the future, and how would that impact you?
Solution
Increase in productivity and resources are the building block for any economy for that matter.
One of the prime reasons why US economy developed in the last century is because of the
importance given to trade and commerce as also industrialisation and optimum usage of
available resources. US had and still has abundance of metals and coal, the driving factors for
any industry. American economy is also one of the most open and most traded with economies
with every single nation being its trade partner. This is also understandable since nearly 40% of
capital used in US is imported. Then during 1940s and 1950s, there was a shift in labour class as
more and more people starting enrolling in higher education. Gradually, labour got more skilled
and productive.
Now, it is eactly the same factors that would result in a falling GDP and growth rate. Although
this would not really happen since the cycle of development is permanent and might take
generations to hit bottom rock, its several factors that would result in falling productivity to be
specific. Resources too should be counted for since their exhaustion can lead to some serious
economic disasters. Imagine what it might be if all coal reserves would suddenly vanish. You
will have each and every industry coming to a halt, there would be continuous electricity cuts,
productivity would go at zero levels and people\'s income would hit rock bottom. So definitely
resources play one of the most crucial parts when it comes to growth rates.
Take the case of productivity. Its the people who contribute towards productivity. The latter is
decided by education levels, population and taxation. Higher education simply leads to higher
levels of productivity. Economic history of US stands as an evidence. The higher the population,
lower is the productivity but only to certain limit. Since employment levels depend on
population, a scarcity in the latter cannot lead to higher growth. Similarly, too high population
leads to lower productivity and per capita income. Lastly is taxation, something that is still being
debated. too high tax levels act as deterrents to income growth, too low taxes inhibit economic
growth..
Two power generating units A and B operate in parallel to supply the.pdf
Two power generating units A and B operate in parallel to supply the power requirements of a
small city. The probability of failure of each unit is 0.1, where the probability that both fail is
0.02.
What is the probability that when there is a power failure only one of the two units will have
failed?
Solution
P(only one of them has failed) = P(Failure of A) + P(failure of B) - 2P(Failure of both)
= 0.1 + 0.1 - 2*0.02
= 0.16.
two frieends are to meet at the library. Each arrives at independent.pdf
two frieends are to meet at the library. Each arrives at independently and randomly selected
times wiithin afixed 1- hour period. Each agree to wait no more than 15 minutes for the other.
find the probability that the meet.
Solution
Let\'s take n = 2 variables ( the two people\' s arrivals ) ;
d = 60 min ( the entire period within they arrive) ;
t = 15/d = 15/60 = 0.25 ( fraction of entire period they wait );
The probability they meet is :
p = nt^(n-1) - (n-1)t^n = 2*0.25^1 - 1*0.25^2 = 0.4375.
Two fair dice are tossed. Let X denote the number appearing on the .pdf
Two fair dice are tossed. Let X denote the number appearing on the first die and Y the number
on the second. Show that X and Y are independent.
Solution
the number on 1st die does not effect the the probability of number on second die ...
Therfore the number appearing on 1st die and number on 2nd are independent events.
Two disks are independantly slected. What is the probability that n.pdf
Two disks are independantly slected. What is the probability that neither contains a missing
pulse if the poisson distribution parameter lamda=.2?
Solution
P(x=0) = e^-2 2^0/0! = e^-2
P(x=0) = e^-2 2^0 / 0! = e^-2
since both are independent !!
the probability that neither contains a missing pulse = e^-2 * e^-2 = 0.0183
thus ans.
Two independent discrete random variables X and Y have marginal dist.pdf
Two independent discrete random variables X and Y have marginal distributions
f1(x) = x/21 and f2(y) = y/36 for certain sets of values x and y. Find the bivariate distribution
f(x, y).
Solution
since the variables are independent, f(x,y)= f(x)* f(y) = x*y/(21*36) = xy/756.
Two friends board an airliner just before departure time. There are .pdf
Two friends board an airliner just before departure time. There are only ten seats left, two of
which are aisle seats. How many ways can the two people arrange themselves in available seats
so that at least one of them sits on the aisle?
Solution
total seats avaiable: 10
2= aisle , 8 = normal
1) both the friends get the aisle seats= 2P2= 2 ways
2) one gets an aisle seat while other gets the normal seat = 2P1x 8P1= 2x8 = 16 ways
Total way s= 2 + 16 = 18 ways.
Two international students were talking in the wake of the Singapore.pdf
Two international students were talking in the wake of the Singapore Air disaster a few years
ago. The first student said she had been intending to fly Singapore Air for the semester break,
but wasn
Solution
Poisson random variables are independent of time since last event..
Two people, both of whom are carriers for a recessive genetic disord.pdf
Two people, both of whom are carriers for a recessive genetic disorder (both are heterozygotes),
have a child. Given that the child is not affected by the disease, what is the probability that
he/she is a heterozygote (and thus carries the gene for the disorder)?
Solution
probability - 1/2.
Two people took turns tossing a fair die until one of them tossed a .pdf
Two people took turns tossing a fair die until one of them tossed a 6. Person A tossed first, B
second. A third, and so on. Given that perosn B threw the first 6, what is the probability that B
obtained the first 6 on her second toss (that is on, on the fourth toss overall)?
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Geometric pmf -> x = n, p(1-p)^n P[6] = probability of rolling a 6 = 1/6 P[x = 4] =
(1/6)(5/6)^3 = 125/1296 = .09645.
Two measures of center for a distribution are 67.0 and 70.7. One of .pdf
Two measures of center for a distribution are 67.0 and 70.7. One of these is the mean and the
other is the median. Which is which? Explain your choice.
Solution
Need more information. If symmetrical Median = Mean. If skewed mean is in
direction of skewness..
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