Let x be a gaussian random variable with the same

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 9999915. The Φ and Q functions are available on many programable calculators and on Internet websites.1 Some numerical values of these functions are given in Tables 6.1 and 6.2, in the appendix. Let µ be any number and σ > 0. If X is a standard Gaussian random variable, and Y = σX + µ, then Y is a N (µ, σ 2 ) random variable. Indeed, 1 u2 fX (u) = √ exp − 2 2π , so by the scaling rule (3.3), 1 v−µ fX σ σ (v − µ)2 1 √ exp − 2σ 2 2πσ fY (v ) = = , so fY is indeed the N (µ, σ 2 ) pdf. Graphically, this means that the N (µ, σ 2 ) pdf can be obtained from the standard normal pdf by stretching it horizontally by a factor σ, shrinking it vertically by a factor σ, and sliding it over by µ. Working in the other direction, if Y is a N (µ, σ 2 ) random variable, then the standardized version − of Y , namely X = Y σ µ , is a standard normal random variable. Graphically, this means that the standard normal pdf can be obtained from a N (µ, σ 2 ) pdf by sliding it over by µ (so it becomes c...
View Full Document

This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

Ask a homework question - tutors are online