## Book: Mathematics Part-II

### Chapter: 13. Probability

#### Subject: Maths - Class 12th

##### Q. No. 14 of Exercise 13.4

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##### 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.

Given: The class of 15 students with their ages.

Form the given information we can draw a table:

 X 14 15 16 17 18 19 20 21 f 2 1 2 3 1 2 3 1

P(X = 14)

P(X = 15)

P(X = 16)

P(X = 17)

P(X = 18)

P(X = 19)

P(X = 20)

P(X = 21)

Hence, the required probability distribution is,

 X 14 15 16 17 18 19 20 21 P(X)

Therefore E(X) is:

E(X) = 17.53

And E(X2) is:

E(X2) = 312.2

Then Variance, Var(X) = E(X2) – (E(X))2

= 312.2 – (17.53)2

= 312.2 – 307.417 ≈ 4.78

And Standard deviation

Standard deviation ≈ 2.19

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