For the probability distribution of a discrete random variable $X$, $E(X) = 5$ and $E(X^2) = 35$, what will be the variance of this distribution? (a) $40$ (b) $30$ (c) $20$ (d) $10$

For the probability distribution of a discrete random variable X, E(X) = 5 and E(X²) = 35, what will be the va

CBSE 2026Set MARCH1 markMCQ

E(X^2)

(a)

10

(b)

4

(c)

40

(d)

16

›Reveal solution

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

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

CBSE 2025Set MARCH1 markMCQ

X

(a)

40

(b)

30

(c)

20

(d)

10

›Reveal solution

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: …

CBSE 2022Set MARCH1 markMCQ

X

(a) 40

(b) 30

(c) 20

(d) 10

›Reveal solution

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. …