A random variable X follows a binomial distribution B(n = 20, p = 0.3). Find the expected value E(X) and variance Var(X).
Answer and explanation
Correct answer: B. E(X) = 6, Var(X) = 4.2
- Step 1: Formula for expected value: E(X) = n p = 20 0.3 = 6.
- Step 2: Formula for variance: Var(X) = n p (1 - p).
- Step 3: Here, 1 - p = 0.7.
- Step 4: Calculate variance: Var(X) = 6 * 0.7 = 4.2.
Answer
E(X) = 6, Var(X) = 4.2.
Why not the others: 'E(X) = 6, Var(X) = 6' assumes variance equals mean (Poisson property, not binomial); 'E(X) = 4.2, Var(X) = 6' reverses mean and variance; 'E(X) = 6, Var(X) = 2.05' calculates standard deviation sqrt(4.2) instead of variance.
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