Q.Mean and variance of a discrete probability distribution are 3 and 7 respectively. What will be $E(X^2)$ for this distribution?

$E(X^2)=\text{Var}(X)+[E(X)]^2=7+9=16$.

The variance of a random variable is $\text{Var}(X)=E(X^2)-[E(X)]^2$. Rearranging, …

Using $V(X) = E(X^2) - [E(X)]^2 = 35 - 25 = 10$, the variance is $10$ — option (d).

GSEB Class-12 Statistics, Random Variable and Discrete Probability Distribution:

The variance of a discrete random variable is: …

Using $V(X)=E(X^2)-[E(X)]^2 = 35-5^2 = \mathbf{10}$.

Given: $E(X)=5$, $E(X^2)=35$.

Step — apply the variance formula. …