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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)/225P(X = x) = C(25, x)/2^{25}. Then which of the following statements are true?

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

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Uncorrelated ⇒ independent

More on this topic

The chapter behind this: Random variables, moments and generating functions — free to read

From Probability › Random variables, distributions, moments, MGF

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