Introduction to Probability · Problem 8.2.1

Central Limit Theorem — Grinstead & Snell

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

Problem

Let

X

be a continuous random variable with mean

\mu = 10

and variance

\sigma^2 = 100/3

. Using Chebyshev's Inequality, find an upper bound for the following probabilities. (a)

P(|X - 10| \geq 2)

. (b)

P(|X - 10| \geq 5)

. (c)

P(|X - 10| \geq 9)

. (d)

P(|X - 10| \geq 20)