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ASSIGNMENT
PROGRAM MCA
SEMESTER FOURTH
SUBJECT CODE & NAME MCA4020- PROBABILITY AND STATISTICS
BK ID B1779
CREDIT & MARKS 4 CREDITS & 60 MARKS
1 Three machines A, B and C produce respectively 60%, 30% and 10% of the total number of items of a
factory. The percentage of defective output of these machines are respectively 2%, 3% and 4%. An
item is selected at random and is found to be defective. Find the probability that the item was
producedby machine C.
Answer: Multiply the respective percentage of production by the percentage of defects for each
machine
A = 60% * 2% = 1.2% of the factory'stotal outputare defectsproducedbyMachine A
B = 30% * 3% = 0.9% of the factory's total outputare defectsproducedbyMachine B
C = 10% * 4% = 0.4% of the factory's total outputare defectsproducedbyMachine C
Therefore the total defects=1.2% + 0.9% + 0.4% = 2.5%
2 Findthe constant k so that

2. F(x,y) = {k(x+1)e-y
, 0<x<1,y>0
0 elsewhere
Is a jointprobabilitydensityfunction.Are X and Y independent?
Answer: Probability density function:- In probability theory and statistics, given two jointly distributed
random variables X and Y, the conditional probability distribution of Y given X is the probability
distribution of Y when X is known to be a particular value; in some cases the conditional probabilities
may be expressed as functions containing the unspecified value x of X as a parameter. In case that both
"X" and "Y" are categorical variables, a conditional probability table is typically used to represent the
conditional probability.The conditional distribution
3 The data shows the distributionofweight ofstudents of1st standard of a school. Findthe quartiles.
Class
Interval
13-18 18-20 20-21 21-22 22-23 23-25 25-30
Frequency 22 27 51 42 32 16 10
Answer:If a data setof scoresisarranged inascendingorderof magnitude,then:
The medianisthe middle value of the dataset.
The lowerquartile (Q1) isthe medianof the lowerhalf of the data set.
The upperquartile (Q3) isthe medianof the upper
4 Fita trend line to the following data by the freehandmethod:
Year Production of wheat(in
tonnes)
Year Production of wheat(in
tonnes)
1995 20 2000 25
1996 22 2001 23

3. 1997 24 2002 26
1998 21 2003 25
1999 23 2004 24
Answer: Methods of Freehands: It is familiar concept, briefly described for drawing frequency curves. In
case of a time series a scatter diagram of the given observations is plotted against time on the horizontal
axis and a freehand smooth curve is drawn through the plotted points. The curve is so drawn that most
of the points concentrate around the curve, however, smoothness should not be scarified in trying to let
the points exactly fall on the curve. It would be better to draw a straight line through the plotted points
insteadof a curve,if possible.The curve fittedby
5 Let X be a random variable and its probabilitymass functionis
P(x=r) = qr-1
p,r=1,2,3…
Findthe m.g.f. of X and hence it’s mean and variance.
Answer:StandardDeviation:-TheStandardDeviationisameasure of how spreadoutnumbersare.
Its symbol isσ(the greeklettersigma)
The formulaiseasy:it isthe square rootof the Variance.Sonow you ask,"What isthe Variance?"
Variance
6 The diastolic blood pressures of men are distributed as shown in table. Find the standard deviation
and variance.
Pressure 78-80 80-82 82-84 84-86 86-88 88-90
No. of Men 3 15 26 23 9 4
Answer:Givenvaluesare:
Pressure 78-80 80-82 82-84 84-86 86-88 88-90
No. of Men 3 15 26 23 9 4
Difference =2

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