Skip to content
Part BCSIR NET June 2023order-statistics-of-bernoulli

Order statistics of bernoulli

Let X1,X2,X3,X4X_{1}, X_{2}, X_{3}, X_{4} be i.i.d. Bernoulli(1/3) and X(1)≤⋯≤X(4)X_{(1)} \le \cdots \le X_{(4)} the order statistics. Which of the following is true?

  1. A.X(1)X_{(1)} and X(4)X_{(4)} are independent.
  2. B.Expectation of X(2)X_{(2)} is 1/2.
  3. C.Variance of X(2)X_{(2)} is 8/81.✓ Correct
  4. D.X(4)X_{(4)} is a degenerate random variable.

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.

ShareWhatsAppTelegram