Two probability distributionof the discrete random variable X and Y are given below.

Prove that `E(Y^(2))=2E(X)`.

Explanation

Since, we have to prove that, `E(Y^(2))=2E(X)` ltbr gt`E(X)=SigmaXP(X)`
`=0cdot1/5+1cdot2/5+3cdot1/5=7/5`
`rArr 2E(X)=14/5`
`E( Y^(2))=SigmaY^(2)P(Y)`
`=0cdot1/5+1cdot3/10+4cdot2/5+9cdot1/10`
`=3/10+8/5+9/10=28/10=14/5`
`rArr E(Y^(2))=14/5`
From Eqs. (i) and (ii),
`E(Y^(2))=2E(X)` Hence proved.