Introduction to Probability · Problem 8.2.18

Central Limit Theorem — Grinstead & Snell

Mathematics — Probability · law-of-large-numbers-continuous

Problem

(Lamperti) Let

X

be a non-negative random variable. What is the best upper bound you can give for

P(X \geq a)

if you know (a)

E(X) = 20

. (b)

E(X) = 20

and

V(X) = 25

. (c)

E(X) = 20

V(X) = 25

, and

X

is symmetric about its mean.