Question

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(16, 0.25)$ and $Y \sim P(2)$. Then the sum of the variances of $X$ and $Y$ is

• A. 4
• B. 5
• C. 6
• D. 2

Hint:

Variance of Binomial is $np(1-p)$; for Poisson, it equals the mean.

Answer 1

The Correct Option is B

For Binomial distribution $X \sim B(n, p)$, variance = $np(1 - p)$
$\Rightarrow \text{Var}(X) = 16 \cdot 0.25 \cdot 0.75 = 3$
For Poisson distribution $Y \sim P(\lambda)$, variance = $\lambda = 2$
Sum of variances = $3 + 2 = 5$