If the standard deviation of the random variable X is `sqrt(3pq)` and mean is 3p then `E(x^(2))`= . . .

Options

A. `3pq + 3q^(2)`
B. `3p(1+2p)`
C. `3pq + 3p^(2)`
D. `3p(1+2p)`

Answer

B

Explanation

We have standard deviaiton of `X = sqrt(3pq)`
`rArr Var (X) = 3pq`
and mean `E(X) = 3p`
Now `3qp = E(x^(2)) - (3p^(2)) " "(because Var (x) = E(X^(2)) - (E(X)^(2)))`
`rArr " "E(X^(2)) = 3pq + 9p^(2)`
` = 3p (1-p) + 9p^(2)" "(because p + q=1)`
`= 3p - 3p^(2) + 9p^(2)`
`rArr 3p + 6p^(2) rArr 3p(1+2p)`