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Description
PROGRAM MCA
SEMESTER III
COURSE CODE & NAME DCA7101 – PROBABILITY AND STATISTICS
SETI
 Bag I contain 3 red and 4 black balls and Bag II contain 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red. Find the probability that the transferred ball is black.
Solution: Step 1: Consider all possible events for transferring balls.
Given that,
Bag I contains 3 red and 4 black balls.
Bag II contains 4 red and 5 black balls.
Let E1, E2, E3, E, be events such that,
E1: Both transferred balls from Bag I to Bag II are red.
E2:
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 A random variable has the following probability distribution
X  0  1  2  3  4  5  6  7 
P(X=x)  0  a  2a  2a  3a  a^2  2a^2  7a^2 + a 
Find
(i) the value of ‘a’
(ii) P [1.5<X<4.5/ X>2]
(iii) E(X)
(i)
Solution: Since it is a probability distribution, so, sum of all probabilities must be 1
 The daily earning of a vendor for a period of 43 days are given below
Daily earning (Rs.)

118
126

127
135

136
144

145
153

154
162

163
171

172
180

No. of days  3  8  9  12  5  4  2

Calculate Standard Deviation and coefficient of variation.
Solution:
Daily earnings  f  x  fx  (xx̄)  F(x x̄)  f(x x̄)^{2} 
118126  3  122  366  23.86  71.58  1707.90 
127135  8  131  1048  14.86  118.88  1766.56 
136144  9  140  1260  5.86  52.74  309.06 
145153  12  149  1788  3.14  37.68  118.32 
154162  5  158  790  12.14  60.7  736.90 
163171  4  167  668  21.14  84.56  1787.60 
172180  2  176  352  30.14  60.28  1816.84 
Fx=43  ∑fx=6272  ∑f(x x̄)^{2}=8243.18 
Mean x̄=
SETII
 Suppose that a manufactured product has 2 defects per unit of product inspected. Using Poisson’s distribution, calculate the probabilities of finding a product without any defect, 3 defects, and 4 defects. (Given)
Solution:
Given:
A manufactured product has 2 defects per unit of product inspected
To find:
The probabilities of finding a product with
 out any defect
 Compute the regression equation of Y on X and regression equation of X on Y on the basis of the following information
X  Y  
Mean  40  45

Standard Deviation  10  9 
The correlation coefficient between X and Y is 0.50. Also estimate the value of Y for X = 48, using the appropriate regression equation.
Answer:
Given that,
The line of regression fo
 The following data relate to the prices and quantities of 4 commodities in the years 1982 and 1983. Construct the following index numbers of price for the year 1983 by using 1982 as base year.
(i) Laspeyre’s Index
(ii) Paasche’s Index
(iii) Fisher’s Index
Commodit Y

1982  1983


Price  Quantity  Price  Quantity  
A  5  100  6  150  
B  4  80  5  100  
C  2.5  60  5  72  
D  12  30  9  33  
Solution:
Commodit Y

1982  1983

P1q0  P0q0  P1q1  P0q1  
Price(P0)  Quantity(Q0)  Price(P1)  Quantity(Q1)  
A  5  100  6  150  600  500  900  750 
B  4  80  5  100  400  320  500  400 
C  2.5  60  5  72  300  150  360  180 
D  12  30  9  33  270  360  297  396 
Total  1570  1330  2057  1726 