1 some numerical values of these functions are given

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: ift the graph horizontally by b (to the right if b > 0 or to the left if b < 0.) Here is a derivation of the scaling rule (3.3). Express the CDF of Y as: FY (v ) = P {aX + b ≤ v } = P X≤ v−b a = FX v−b a , and then differentiate FY (v ) with respect to v , using the chain rule of calculus and the fact FX = fX , to obtain: v−b 1 fY (v ) = FY (v ) = fX . a a Section 3.2 recounts how the mean, variance, and standard deviation of Y are related to the mean, variance, and standard deviation of X, in case Y = aX + b. These relations are the same ones discussed in Section 2.2 for discrete-type random variables, namely: E [Y ] = aE [X ] + b Var(Y) = a2 Var(X ) σY = aσX . Example 3.6.1 Let X denote the pdf of the high temperature, in degrees C (Celsius), for a certain day of the year in some city. Let Y denote the pdf of the same temperature, but in degrees F (Fahrenheit). The conversion formula is Y = (1.8)X + 32. This is the linear transformation that maps zero degrees C to 32 degrees F and 100 degrees C to 212 degrees F. (...
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