Consider the probability distribution of a random variable X

Calculate
(i) `V( X/2)` (ii) Variance of X.

Explanation

We have

Var(X)=E`(X^(2))-[E(X)]^(2)`
where, `E( X)=mu=sum_(i=1)^(n)x_(i)P_(i)(xi)`
and `E(X^(2))=sun_(i=1)^(n)x_(i)P_(i)(xi)`
`thereforeE(X)=0+0.25+0.6+0.6+0.60=2.05`
`E(X^(2))=0+0.25+1.2+1.8+2.40=5.65`
(i) `V(X/2)=1/4V(X)=1/4[5.65-(2.05)^(2)]`
`=1/4[56.65-4.2025]=1/4xx 1.4775 = 0.361875`
(II) V(X) = 1.4475