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+2q)`

Answer

B

Explanation

We have standard deviation of `X=sqrt(3pq)`
`implies Vax(X)=3pq`
and mean, `E(X)=3p`
Now, `3pq=E(x^(2))-(3p^(2))" "(becauseVar(X)=E(X^(2))-(E(X)^(2)))`
`impliesE(X^(2))=3pq+9p^(2)=3p(1-p)+9p^(2)" "(becausep+q=1)`
`=3p-3p^(2)+9p^(2)`
`implies3p+6p^(2)implies3p(1+2p)`