Introduction to Probability · Problem 8.2.14

Central Limit Theorem — Grinstead & Snell

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

Problem

Let

X

be a continuous random variable normally distributed on

(-\infty, +\infty)

with mean 0 and variance 1. Using the normal table provided in Appendix A, or the program NormalArea, find values for the function

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

x

increases from 0 to 4.0 in steps of .25. Note that for

x \geq 0

the table gives

\mathrm{NA}(0, x) = P(0 \leq X \leq x)

and thus

P(|X| \geq x) = 2(.5 - \mathrm{NA}(0, x))

. Plot by hand the graph of

f(x)

using these values, and the graph of the Chebyshev function

g(x) = 1/x^2

, and compare (see Exercise 3).