← All problems

415.Fixed Points of a Random Function

★★★
classical probabilityCh. 3 — Discrete Distributions and Moments444+ Problems in Probability
Let FnF_n be the number of fixed points of a uniformly random function f:{1,…,n}→{1,…,n}f : \{1,\dots,n\} \to \{1,\dots,n\}. Find lim⁡n→∞P[Fn=5]\lim_{n\to\infty} P[F_n = 5].

Sign in to submit an answer and track it toward your stats.

Sign in
← Sum and Difference, Perfectly CorrelatedThe Cheapest MGF →

Want timed drills, mental math, and a market-making game too? Try the full practice suite →