Introduction to Probability · Problem 8.2.3

Central Limit Theorem — Grinstead & Snell

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

Problem

Let

X

be the random variable of Exercise 2. (a) Calculate the function

f(x) = P(|X - 10| \geq x)

. (b) Now graph the function

f(x)

, and on the same axes, graph the Chebyshev function

g(x) = 100/(3x^2)

. Show that

f(x) \leq g(x)

for all

x > 0

, but that

g(x)

is not a very good approximation for

f(x)