Question

The Variance of the following probability distribution of X is

X	\(0\)	\(1\)	\(2\)	\(3\)
P(X)	\(q^3\)	\(3q^2p\)	\(3qp^2\)	\(p^3\)

where \(0 < p < 1,q = 1-p\)

• A. \(3p^2q\)
• B. \(3pq\)
• C. \(3pq^2\)
• D. \(3q\)

Hint:

This is a binomial distribution with n = 3.

Answer 1

The Correct Option is B

Step 1: Sum of Bernoulli trials:
$X$ is the sum of 3 independent trials, each with variance $pq$.

Step 2: Add:
Variances add for independent trials: $pq+pq+pq=3pq$.

Step 3: Select:
Option (B). The others do not reduce to $3pq$.

Final Answer:
Each of the three trials contributes pq. \[ \boxed{B} \]