Part BCSIR NET December 2025root-5-splits-the-binomial-support-between-2-and-3-not-at-a-rounder-number

Root 5 splits the binomial support between 2 and 3 not at a rounder number

Let $X_{1}, X_{2}, \dots$ be a sequence of independent and identically distributed random variables having Binomial(3, 1/4) distribution. For j=1,2,…, define $Y_{j} = 1$ if $X_{j} \le \sqrt{5}$ , and 0 otherwise. If $(1/n)\sum_{j=1}^n$ $Y_{j}^{2}$ converges almost surely to a constant c as $n \to \infty$ , then the value of c equals

A.1/64
B.37/64
C.63/64✓ Correct
D.27/32

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

Root 5 splits the binomial support between 2 and 3 not at a rounder number

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