Question

Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below: 

X = x	1	2	3
P(X)	`1/5`	`2/5`	`2/5`

Answer 1

`E(X)=sumx_iP(x_i)`

 = `1(1/5)+2(2/5)+3(2/5)`

= `(1+4+6)/5`

= `11/5`

= 2.2

`E(X^2)=sumx_i^2P(x_i)`

= `1^2(1/5)+2^2(2/5)+3^2(2/5)`

= `(1+8+18)/5`

= `27/5`

= 5.4

Var(X) = E(X²) − [E(X)]²

 = 5.4 − (2.2)²

= 5.4 − 4.84

= 0.56

S.D. = `sqrt(Var (X))` 

= `sqrt0.56`

= 0.7483