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Question -

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.



Answer -

Given the class of 15students with their ages.

Form the given data wecan draw a table

X

14

15

16

17

18

19

20

21

f

2

1

2

3

1

2

3

1

P(X = 14) = 2/15

P(X = 15) = 1/15

P(X = 16) = 2/15

P(X = 17) = 3/15

P(X = 18) = 1/15

P(X = 19) = 2/15

P(X = 20) = 3/15

P(X = 21) = 1/15

Hence, the requiredprobability distribution is,

X

14

15

16

17

18

19

20

21

P (X)

2/15

1/15

2/15

3/15

1/15

2/15

3/15

1/15

Therefore E(X) is:

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