Question

Find the expected value and variance of r.v. X whose p.m.f. is given below.

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

Answer 1

E(X) = `sum_("i" = 1)^3 x_"i"* "P"(x_"i")`

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

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

= `11/5`

E(x²) = `sum_("i" = 1)^3 x_"i"^2* "P"(x_"i")`

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

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

= `27/5`

∴ Var(X) = E(X²) − [E(X)]²

= `27/5 - (11/5)^2` 

= `14/25`