Consider the probability distribution of a random variable X:

Calculate (i) (ii) Variance of X.

We have

Var(X)=E(X²)-[E(X)]²

Where,

And

∴0+0.25+0.6+0.6+0.60= 2.05

And E(X)²=0+0.25+1.2+1.8+2.40=5.65

(i)

As we know Var(ax) = a² var(x)

(ii) V(X)

Var(X)=E(X²)-[E(X)]²

= 5.65 – (2.05)²

= 5.65 - 4.2025

= 1.4475