Introduction to Probability · Problem 8.1.9

Law of Large Numbers — Grinstead & Snell

Mathematics — Probability · chebyshev-inequality

Problem

In Exercise 6.2.15, you showed that, for the hat check problem, the number

S_n

of people who get their own hats back has

E(S_n) = V(S_n) = 1

. Using Chebyshev's Inequality, show that

P(S_n \geq 11) \leq .01

for any

n \geq 11