GATE 2023 BM – Question 12

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

For a binomial random variable X, which proposed pair of expectation E(X) and variance Var(X) cannot be true?

E(X)=20, Var(X)=16
E(X)=6, Var(X)=5.4
E(X)=10, Var(X)=15
E(X)=64, Var(X)=12.8

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Correct answer: (C) E(X)=10, Var(X)=15

Explanation

For X binomial with parameters n and p, mean=np and variance=np(1−p)=mean×(1−p). Variance cannot exceed the mean. C proposes fifteen greater than ten and is impossible. A, B and D correspond respectively to p=.2,.1,.8 and integer n=100,60,80.

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