Suppose that X and Y are random variables such that E(Y X) = 7 -.pdf
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Suppose that X and Y are random variables such that E(Y | X) = 7 - (1/4)x E(X | Y) = 10 - Y . Determine the correlation of X and Y . Solution We know that cor(x,y)=cov(x,y)/(v(x)v(y))^.5 here we are given with p@Y/@X and p@X/@Y thus on solving we get cor(x,y) =0.5 here @ =sigma.
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suppose the lifetime of x of an electronic components follows distri.pdf
Suppose the lifetime of a van has a uniform distribution over [3,10]. Mr Smith buys a new
van as soon as his old van either breaks down or reaches the age of 8 years. A new van costs
$20,000 and an additional cost of $1000 is incurred whenever a van breaks down. Assume
that a T years old car in working order has an expected resale value of 20,000[(1000T)/2].
What is Mr Smith\'s long-run average cost?
Solution
L= Lifetime of the van
L~ U(0,10)
I[A] is the indicator function which takes the value 1 if A is true and 0 otherwise.
Long run cost of Mr. Smith
= Cost incurred* I[ old van breaks down before reaching the age of 8 years] + Cost incurred * [
old van reaches the age of 8 years]
Thus Expected long run cost
= Cost Incurred* P[old van breaks down before reaching the age of 8 years]+ Cost incurred *
P[old van survived reaches the age of 8 years]
= $ 21000* P[ L < 8 ] + ${20000-1000*8/2}* P[ L > 8]
= $ 21000* (8-3)/(10-3) + $16000 * (10-8)/(10-3)
= $ 21000* 5/7 + $ 16000* 2/7
= $ 15000 + $ 4571.4
=$ 19571.4
Please rate and reward :).
Suppose the market for computer chips is dominated by two firms Int.pdf
Suppose the market for cigarettes is characterized by the following information :
Qd= 70-5P (demand)
Qs = 3P-10 (Supply)
Suppose the government impose a sales tax of $2 per unit. Calculate the Dead-Weight-Loss due
to the sales tax.
(Note : P= Price per unit; Qd= thousands of units demanded; Qs = thousands of units Supplied)
Solution
Let us first find the equilibrium price an quantity for the market.
The demand and supply function for the cigarettes is given as,
Qd = 70.
Suppose the lifetime of a device T has an exponential distribution w.pdf
Suppose the life of a particular brand of calculator battery is approximately normally distributed
with a mean of 75 hours and a standard deviation of 10 hours. What is the probability that a
single battery randomly selected from the population will have a life between 70 and 80 hours?
Solution
using a Z score we get Zup = (80-75)/10 = .5 and Zdown = (70-75)/10 = -.5 so
using a table we know that the probability of being between the mean and .5 standard deviations
from the mean is .1915 and doubling that for the other side gives us a probability of .383.
Suppose that you are presented with three urns. Each urn contains fi.pdf
Suppose that you are presented with three urns. Each urn contains five indistinguishable balls,
except that one is green and four are red. You get to draw once from each urn. What is the
probability that you get an odd number of green balls? Also: What type of random variable is
involved in this problem?
Solution
P(odd no of green balls)=1-((1/5)^2*(4/5))=.97 discrete random variable.
Suppose that you are designing a new video streaming service. You ha.pdf
Suppose that you are designing a new video streaming service. You have chosen the DASH
system (Dynamic Adaptive Streaming over HTTP), so you have created a method to store
different versions of the video encoded at different bitrates. This allows your end-user to select
the bitrate they want to see when they play the video. Explain how this system can be utilized to
overcome network related issues, especially if your service controls the video player application.
Describe the interaction that should occur as the client program encounters common network
issues like delay, jitter or packet loss.
Solution
MPEG-DASH builds on the already excellent adaptive streaming technologies deployed today.
The MP4 File Format (based on the ISO Base Media File Format) enables common encryption to
allow delivery of content to a wide range of devices with various DRM schemes. MPEG-DASH
also allows multiple language versions of the same content to be delivered thus enlarging target
audiences. Whether consuming traffic from a service provider’s own content offering, or using a
new over-the-top service, video consumption to IP-enabled devices is driving up traffic on
operators’ networks. Building out new capacity to cope with today’s demands and the predicted
growth over the coming years is prohibitively expensive, yet consumers continue to expect
higher quality IP video without a corresponding hike in broadband access charges.
MPEG-DASH will help to overcome some of the challenges of other adaptive streaming formats
and provides service providers with the confidence coming from embracing a truly global
standard.
What MPEG-DASH aims to do is simplify the delivery landscape and help realize the promise
of adaptive streaming.
MPEG-DASH enables the delivery of content to all devices. One of the major challenges facing
content and service providers is the fragmentation of devices. It is no longer enough to create a
single version of a video asset for presentation on the household TV. Multiple viewing devices
with differing screen sizes receive content over networks with capacities that vary over time; a
Smartphone on a 3G mobile network requires a completely different asset than the 50” HDTV in
the living room. MPEG-DASH reduces cost at every step of the chain from content preparation,
hosting, caching to final delivery. MPEG-DASH, as an http adaptive streaming technology,
promises to reduce complexity by allowing the receiving device to select which resolution and
bitrate stream to view, and the ability to change the choice over time as network conditions
demand. This will allow content providers to concentrate on generating a fixed number of
choices for each asset, greatly simplifying their workflow. It will also allow business models to
expand to cater for content even further down the “tail”. It will also allow delivery of content to
homes that were previously out of reach commercially..
Suppose that X1 equals 4. What are the values for d1+ and d1- in the.pdf
Suppose that X1 equals 4. What are the values for d1+ and d1- in the following constraint?
X1 + d1-- d1+ = 10
Solution
Hi,
The correct answer is as follows:
If we have the following goal constraint: x1 + d1 - – d1+ = 10 If x1 = 4, then it must be true that
d1 - = 6 and d1+ = 0, so they sum to 10..
Suppose that Y1,Y2,...,Yn is a random sample from a probability dens.pdf
Suppose that Y1,Y2,...,Yn is a random sample from a probability denstiy function in the (one
parameter) exponential family so that
f(y|?) = { a(?)b(y)e-[c(?)d(y)], a=y=b .... 0, elsewhere}
where a and b do not depend on ?. Show that S(1 to n) d(Yi) is sufficient for ?.
Solution
what is the question mark given in the question i cant able to determine an answer
with that question mark can u repost the question there.
Suppose that Y1,....,Yn denote a random sample from the Poisson dist.pdf
The document discusses the Poisson distribution and finding the maximum likelihood estimator for P(Y=0). The Poisson distribution models the number of events occurring in a fixed interval of time or space if these events occur with a known average rate and independently of the time since the last event. The maximum likelihood estimator for P(Y=0), the probability of observing no events, is e^(-λ) where λ is the mean of the Poisson distribution.
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suppose the lifetime of x of an electronic components follows distri.pdf
Suppose the lifetime of a van has a uniform distribution over [3,10]. Mr Smith buys a new
van as soon as his old van either breaks down or reaches the age of 8 years. A new van costs
$20,000 and an additional cost of $1000 is incurred whenever a van breaks down. Assume
that a T years old car in working order has an expected resale value of 20,000[(1000T)/2].
What is Mr Smith\'s long-run average cost?
Solution
L= Lifetime of the van
L~ U(0,10)
I[A] is the indicator function which takes the value 1 if A is true and 0 otherwise.
Long run cost of Mr. Smith
= Cost incurred* I[ old van breaks down before reaching the age of 8 years] + Cost incurred * [
old van reaches the age of 8 years]
Thus Expected long run cost
= Cost Incurred* P[old van breaks down before reaching the age of 8 years]+ Cost incurred *
P[old van survived reaches the age of 8 years]
= $ 21000* P[ L < 8 ] + ${20000-1000*8/2}* P[ L > 8]
= $ 21000* (8-3)/(10-3) + $16000 * (10-8)/(10-3)
= $ 21000* 5/7 + $ 16000* 2/7
= $ 15000 + $ 4571.4
=$ 19571.4
Please rate and reward :).
Suppose the market for computer chips is dominated by two firms Int.pdf
Suppose the market for cigarettes is characterized by the following information :
Qd= 70-5P (demand)
Qs = 3P-10 (Supply)
Suppose the government impose a sales tax of $2 per unit. Calculate the Dead-Weight-Loss due
to the sales tax.
(Note : P= Price per unit; Qd= thousands of units demanded; Qs = thousands of units Supplied)
Solution
Let us first find the equilibrium price an quantity for the market.
The demand and supply function for the cigarettes is given as,
Qd = 70.
Suppose the lifetime of a device T has an exponential distribution w.pdf
Suppose the life of a particular brand of calculator battery is approximately normally distributed
with a mean of 75 hours and a standard deviation of 10 hours. What is the probability that a
single battery randomly selected from the population will have a life between 70 and 80 hours?
Solution
using a Z score we get Zup = (80-75)/10 = .5 and Zdown = (70-75)/10 = -.5 so
using a table we know that the probability of being between the mean and .5 standard deviations
from the mean is .1915 and doubling that for the other side gives us a probability of .383.
Suppose that you are presented with three urns. Each urn contains fi.pdf
Suppose that you are presented with three urns. Each urn contains five indistinguishable balls,
except that one is green and four are red. You get to draw once from each urn. What is the
probability that you get an odd number of green balls? Also: What type of random variable is
involved in this problem?
Solution
P(odd no of green balls)=1-((1/5)^2*(4/5))=.97 discrete random variable.
Suppose that you are designing a new video streaming service. You ha.pdf
Suppose that you are designing a new video streaming service. You have chosen the DASH
system (Dynamic Adaptive Streaming over HTTP), so you have created a method to store
different versions of the video encoded at different bitrates. This allows your end-user to select
the bitrate they want to see when they play the video. Explain how this system can be utilized to
overcome network related issues, especially if your service controls the video player application.
Describe the interaction that should occur as the client program encounters common network
issues like delay, jitter or packet loss.
Solution
MPEG-DASH builds on the already excellent adaptive streaming technologies deployed today.
The MP4 File Format (based on the ISO Base Media File Format) enables common encryption to
allow delivery of content to a wide range of devices with various DRM schemes. MPEG-DASH
also allows multiple language versions of the same content to be delivered thus enlarging target
audiences. Whether consuming traffic from a service provider’s own content offering, or using a
new over-the-top service, video consumption to IP-enabled devices is driving up traffic on
operators’ networks. Building out new capacity to cope with today’s demands and the predicted
growth over the coming years is prohibitively expensive, yet consumers continue to expect
higher quality IP video without a corresponding hike in broadband access charges.
MPEG-DASH will help to overcome some of the challenges of other adaptive streaming formats
and provides service providers with the confidence coming from embracing a truly global
standard.
What MPEG-DASH aims to do is simplify the delivery landscape and help realize the promise
of adaptive streaming.
MPEG-DASH enables the delivery of content to all devices. One of the major challenges facing
content and service providers is the fragmentation of devices. It is no longer enough to create a
single version of a video asset for presentation on the household TV. Multiple viewing devices
with differing screen sizes receive content over networks with capacities that vary over time; a
Smartphone on a 3G mobile network requires a completely different asset than the 50” HDTV in
the living room. MPEG-DASH reduces cost at every step of the chain from content preparation,
hosting, caching to final delivery. MPEG-DASH, as an http adaptive streaming technology,
promises to reduce complexity by allowing the receiving device to select which resolution and
bitrate stream to view, and the ability to change the choice over time as network conditions
demand. This will allow content providers to concentrate on generating a fixed number of
choices for each asset, greatly simplifying their workflow. It will also allow business models to
expand to cater for content even further down the “tail”. It will also allow delivery of content to
homes that were previously out of reach commercially..
Suppose that X1 equals 4. What are the values for d1+ and d1- in the.pdf
Suppose that X1 equals 4. What are the values for d1+ and d1- in the following constraint?
X1 + d1-- d1+ = 10
Solution
Hi,
The correct answer is as follows:
If we have the following goal constraint: x1 + d1 - – d1+ = 10 If x1 = 4, then it must be true that
d1 - = 6 and d1+ = 0, so they sum to 10..
Suppose that Y1,Y2,...,Yn is a random sample from a probability dens.pdf
Suppose that Y1,Y2,...,Yn is a random sample from a probability denstiy function in the (one
parameter) exponential family so that
f(y|?) = { a(?)b(y)e-[c(?)d(y)], a=y=b .... 0, elsewhere}
where a and b do not depend on ?. Show that S(1 to n) d(Yi) is sufficient for ?.
Solution
what is the question mark given in the question i cant able to determine an answer
with that question mark can u repost the question there.
Suppose that Y1,....,Yn denote a random sample from the Poisson dist.pdf
The document discusses the Poisson distribution and finding the maximum likelihood estimator for P(Y=0). The Poisson distribution models the number of events occurring in a fixed interval of time or space if these events occur with a known average rate and independently of the time since the last event. The maximum likelihood estimator for P(Y=0), the probability of observing no events, is e^(-λ) where λ is the mean of the Poisson distribution.
Suppose that Y1 and Y2 are independent exponentially distributed ran.pdf
Suppose that Y1 and Y2 are independent exponentially distributed random variables, both with
mean B, and define U1=Y1+Y2 and U2=Y1/Y2 a, show that the joint density of (U1,U2 is
FU1,U2 (U1,U2) = (1/bexp2) u1 e exp(-u1/b) 1/(1+u2)exp2, 0 smaller then u1, 0smaller then
u2 o elsewhere b. are u1 and u2 independent?
Solution
i think there is something missing in the question. can u please coment on it
whether if its true.
Suppose that Y is an exponential random variable with = 2. Find P.pdf
Suppose that Y is an exponential random variable with = 2.
Find P[Y > E(Y) + 2 Var(Y)]
Solution
E(Y )=1/=1/2
Var(Y )=1/ ^2=1/4
P[Y > E(Y ) + 2 + Var(Y )]=P[Y > 1/2+ 2 + 1/4]=P[Y >2.75]
=integral from 2.75 to ( e^(-?t))dt
=[-e^(-t)/] from 2.75 to =e^(-(2.75))
=e^(-2(2.75))=e^(-(5.5))=0.00409.
Suppose that X is a r.v. whose moment generating function is m(thet.pdf
Suppose that X is a r.v. whose moment generating function is: m(theta) = 1/5e^theta
2/5e^(4theta) 2/5e^(8theta), theta from negative infinity to infinity. Find the values (range) of X
and its probability distribution
Solution
From the moment generating function, it can be easily recognized that X is a
discrete distribution with 3 possible value 1, 4 and 8 associated with the possibilities of 1/5, 2/5
and 2/5 respectively; X=1 with p=1/5, X=4 with p=2/5, X=8 with p=2/5..
Suppose that X and Y are independent geometric random variables wit.pdf
Suppose that X and Y are independent geometric random variables with common probability
mass function p(i) = P(X = i) = P(Y = i) = p(1 - p)^(i-1) with i = 1, 2, ... Find the probability
mass function for the random variable X + Y .
Solution
P(X+Y=n)
=sum from 0 to n P(X=k).P(Y=n-k)
=sum from 0 to n p^2(1-p)^(k-1)(1-p)^(n-k-1)
=sum from 0 to n p^2(1-p)^(n-2)
=np^2(1-p)^(n-2).
Suppose the following bond quotes for IOU Corporation appear in the .pdf
Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s
newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2015.
What is the yield to maturity of the bond? What is the current yield?Company (Ticker)
CouponMaturity Last Price Last Yield EST Vol (000s)IOU (IOU) 5.7Apr 19,
2028 108.96 ?? 1,827
Solution.
Suppose the density function of a continuous random Variable X is.pdf
Suppose the density function of a continuous random Variable X is:
f(X) = AX^(-1/2) where 4 ≤ X ≤ 25.
a.) Find the value of the constant A so that f(X) is a PROPER probability function.
b.) Find CDF(X), E(X^2), V(X), σ(X)
c.) Find P(9 ≤ X ≤ 16).
Solution
b)
CDF= integration (1/6)*X^(-1/2) from 4 to x where 4.
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Suppose that Y1 and Y2 are independent exponentially distributed ran.pdf
Suppose that Y1 and Y2 are independent exponentially distributed random variables, both with
mean B, and define U1=Y1+Y2 and U2=Y1/Y2 a, show that the joint density of (U1,U2 is
FU1,U2 (U1,U2) = (1/bexp2) u1 e exp(-u1/b) 1/(1+u2)exp2, 0 smaller then u1, 0smaller then
u2 o elsewhere b. are u1 and u2 independent?
Solution
i think there is something missing in the question. can u please coment on it
whether if its true.
Suppose that Y is an exponential random variable with = 2. Find P.pdf
Suppose that Y is an exponential random variable with = 2.
Find P[Y > E(Y) + 2 Var(Y)]
Solution
E(Y )=1/=1/2
Var(Y )=1/ ^2=1/4
P[Y > E(Y ) + 2 + Var(Y )]=P[Y > 1/2+ 2 + 1/4]=P[Y >2.75]
=integral from 2.75 to ( e^(-?t))dt
=[-e^(-t)/] from 2.75 to =e^(-(2.75))
=e^(-2(2.75))=e^(-(5.5))=0.00409.
Suppose that X is a r.v. whose moment generating function is m(thet.pdf
Suppose that X is a r.v. whose moment generating function is: m(theta) = 1/5e^theta
2/5e^(4theta) 2/5e^(8theta), theta from negative infinity to infinity. Find the values (range) of X
and its probability distribution
Solution
From the moment generating function, it can be easily recognized that X is a
discrete distribution with 3 possible value 1, 4 and 8 associated with the possibilities of 1/5, 2/5
and 2/5 respectively; X=1 with p=1/5, X=4 with p=2/5, X=8 with p=2/5..
Suppose that X and Y are independent geometric random variables wit.pdf
Suppose that X and Y are independent geometric random variables with common probability
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Solution
P(X+Y=n)
=sum from 0 to n P(X=k).P(Y=n-k)
=sum from 0 to n p^2(1-p)^(k-1)(1-p)^(n-k-1)
=sum from 0 to n p^2(1-p)^(n-2)
=np^2(1-p)^(n-2).
Suppose the following bond quotes for IOU Corporation appear in the .pdf
Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s
newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2015.
What is the yield to maturity of the bond? What is the current yield?Company (Ticker)
CouponMaturity Last Price Last Yield EST Vol (000s)IOU (IOU) 5.7Apr 19,
2028 108.96 ?? 1,827
Solution.
Suppose the density function of a continuous random Variable X is.pdf
Suppose the density function of a continuous random Variable X is:
f(X) = AX^(-1/2) where 4 ≤ X ≤ 25.
a.) Find the value of the constant A so that f(X) is a PROPER probability function.
b.) Find CDF(X), E(X^2), V(X), σ(X)
c.) Find P(9 ≤ X ≤ 16).
Solution
b)
CDF= integration (1/6)*X^(-1/2) from 4 to x where 4.
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Agenda
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For Upcoming Meetups Join Mysore Meetup Group - https://meetups.mulesoft.com/mysore/YouTube:- youtube.com/@mulesoftmysore
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