A random variable X takes values 1,2,3 and 4 with probabilities `(1)/(6),(1)/(3),(1)/(3),(1)/(6)` respectively, then its mean and variance is equal to

Options

A. `5/2,(11)/(12)`
B. `5/2,(11)/(16)`
C. `5/3,(11)/(16)`
D. `5/3,(11)/(12)`

Answer

A

Explanation

Mean `=E(X)=Sigmax_i.P(x_i)=1/6(1)+1/3(2)+1/3(3)+1/6(4)`
`=1/6+2/3+1+4/6=(1+4+6+4)/6=(15)/6=5/2`
Variance `=Sigmax_i^2.P(x_i)-[E(X)]^2`
`=1/6(1)^2+1/3(2)^2+1/3(3)^2+1/6(4)^2-(5/2)^2`
`=1/6+4/3+9/3+(16)/6-(25)/4`
`=(2+16+36+32-75)/(12)=(86-75)/(12)=(11)/(12)`