Part CCSIR NET December 2023binomial-symmetry

Binomial symmetry

Let X be a discrete random variable with support {0, 1, …, 25} and $P (X = x) = C (25, x) / 2^{25}$ . Then which of the following statements are true?

A.The distributions of X − 12.5 and 12.5 − X are identical
B.P(X ≤ 4) = P(X ≥ 22)
C.The coefficient of variation (in percentage) of X is 20
D.P(X ≤ 4.9) = P(X ≥ 20.1)

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Related counterexample: Uncorrelated ⇒ independent

Binomial symmetry

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