Question

The probability distribution of a r.v. X is given below:

X	0	2	4
p	`1/5`	`3/5`	`1/5`

Find the standard deviation of X.

Answer 1

E(X) = `sump_ix_i`

= `(0)(1/5) + (2)(3/5) + (4)(1/5)`

= `0 + 6/5 + 4/5`

= `10/5`

= 2

E(X²) = `sump_ix_i^2`

= `(0)(1/5) + (4)(3/5) + (16)(1/5)`

= `0 + 12/5 + 16/5`

= `28/5`

Var (X) = E(X²) – [E(X)]²

= `28/5 - 4`

= `8/5`

= 1.6

∴ S.D (σ_x) = `sqrt(Var(X))`

= `sqrt(1.6)`

= 1.265