Q.If $X$ is a random variable such that $E(X) = 5$ and $Var(X) = 4$, find $E(X^2)$.
(A) 20 (B) 25 (C) 29 (D) 9

The relation between $E(X^2)$, $E(X)$ and $Var(X)$ follows directly from the variance formula rearranged for $E(X^2)$.

Step 1 — Rearrange the variance formula. Since $Var(X) = E(X^2) - [E(X)]^2$,

Step 2 — Substitute the given values.

Dual-solve check. Working backwards from option (C): if $E(X^2)=29$ and $E(X)=5$, then $Var(X)=29-25=4$, which matches the given variance — confirming (C) is correct.

Why the other options are wrong:

• (A) 20 — not a meaningful combination of the given values; likely from confusing multiplication with the correct addition.
• (B) 25 — this is just $[E(X)]^2$ with the variance term dropped entirely.
• (D) 9 — this looks like a sign error in rearranging the formula (subtracting the variance instead of adding it).

Subtracting the variance instead of adding it when rearranging $Var(X)=E(X^2)-[E(X)]^2$ for $E(X^2)$ — the correct rearrangement is $E(X^2) = Var(X) + [E(X)]^2$, addition not subtraction.