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Part CCSIR NET June 2025the-binomial-parameter-is-the-first-mean-over-the-total-not-the-ratio-of-the-two

The binomial parameter is the first mean over the total not the ratio of the two

Let X and Y be independent Poisson random variables with means 4 and 2, respectively. Then, which of the following statements are true?

  1. A.The conditional distribution of X given X + Y = 3 is Binomial(3, 1/3)
  2. B.P(X ≤ 1 | X + Y = 3) = 7/27✓ Correct
  3. C.E(X | X + Y = 3) = 2✓ Correct
  4. D.The value of the characteristic function of X + Y at the point t=πt = \pi is e−12e^{-12}✓ 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: The maximum of independent exponentials is exponential

More on this topic

The chapter behind this: The standard distributions — free to read

From Probability › Standard discrete and continuous distributions

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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