Part BCSIR NET June 2025the-state-space-is-the-2025-residues-not-the-2024-step-values

The state space is the 2025 residues not the 2024 step values

Let $Z_{1}, Z_{2}, \dots$ be a sequence of independent and identically distributed random variables having discrete uniform distribution over {1, 2, …, 2024}. Let $Y_{n} = \sum_{i}$ ₌ $_{1}^{n} Z_{i}, n \geq 2$ . Further, let $X_{n}$ be the remainder when $Y_{n}$ is divided by 2025. Then, which of the following statements is true?

A. $l i m_{n} \to \infty P (X_{n} = 0) = 1/2026$
B. $l i m_{n} \to \infty P (X_{n} = 0) = 1/2025$ ✓
C. $l i m_{n} \to \infty P (X_{n} = 0) = 1/2024$
D. $l i m_{n} \to \infty P (X_{n} = 0) = 1/2023$

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 standard counterexample.

See pricing

50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

The state space is the 2025 residues not the 2024 step values

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