Introduction to Probability · Problem 8.2.4

Central Limit Theorem — Grinstead & Snell

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

Problem

Let

X

be a continuous random variable with values exponentially distributed over

[0, \infty)

with parameter

\lambda = 0.1

. (a) Find the mean and variance of

X

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

P(|X - 10| \geq 2)

P(|X - 10| \geq 5)

P(|X - 10| \geq 9)

, and

P(|X - 10| \geq 20)

. (c) Calculate these probabilities exactly, and compare with the bounds in (b).