Question

If the mean and variance of a binomial variable X are 2.4 and 1.44 respectively, then the parameters \( n \) and \( p \) are respectively:

• A. \( \frac{6}{5}, \frac{2}{5} \)
• B. \( \frac{3}{5}, \frac{3}{5} \)
• C. \( \frac{6}{5}, \frac{3}{5} \)
• D. \( \frac{8}{5}, \frac{1}{3} \)

Hint:

For binomial distributions, use the formulas for the mean and variance to solve for \( n \) and \( p \).

Answer 1

The Correct Option is A

The mean \( \mu \) and variance \( \sigma^2 \) of a binomial distribution are given by: \[ \mu = np \quad \text{and} \quad \sigma^2 = np(1 - p) \] Using the given values \( \mu = 2.4 \) and \( \sigma^2 = 1.44 \), we solve for \( n \) and \( p \). The solution gives \( n = \frac{6}{5} \) and \( p = \frac{2}{5} \).