A discrete random variable X follows a binomial distribution B(12, 0.25). What is the variance of X?

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Question

A discrete random variable X follows a binomial distribution B(12, 0.25). What is the variance of X?

Accepted Answer

Var(X) = 2.25 — For X ~ B(n, p), Var(X) = np(1 − p) = 12 × 0.25 × 0.75 = 2.25. Option B uses only np = 3, which gives the mean not the variance. Option C uses only p = 0.25. Option D uses n(1 − p) = 9, omitting the factor p.

Answer

Var(X) = 3.00

Answer

Var(X) = 2.25

Answer

Var(X) = 0.25

Answer

Var(X) = 9.00

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