Question

The mean and variance of a random variable \( X \) having binomial distribution are 4 and 2 respectively, then \( P(X = 1) \) is:

• A. \( \frac{3}{5} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{1}{8} \)
• D. \( \frac{5}{12} \)

Hint:

For binomial distributions, use the formulas for mean and variance to find \( n \) and \( p \), then use the binomial probability formula to find specific probabilities.

Answer 1

The Correct Option is C

Step 1: For a binomial distribution, the mean \( \mu = np \) and variance \( \sigma^2 = np(1 - p) \). Given the mean and variance, solve for \( n \) and \( p \).
Step 2: Use the binomial probability formula to find \( P(X = 1) \).

Final Answer: \[ \boxed{\frac{1}{8}} \]