STA213lecture5.notes

STA213lecture5.notes - Todays outline: pp 47-55 Examples of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Todays outline: pp 47-55 Examples of variable transformation One-to-one transformations Theorems Example 1: Exponential distn [similar to HW 1.53, 1.55] We are given a random variable X with pdf f X ( x ) = exp(- x ) , x > . We say that X Exp ( ) is exponentially distributed with parameter (also called rate) . What is the cdf of X ? What is the pdf of Y = 2 X ? How about Z = X ? P ( Y < y ) = P (2 X < y ) = P ( X < y/ 2) = Z y/ 2 f X ( x ) dx = 1- exp(- y/ 2) , P ( Z < z ) = 1- exp(- z ) . Differentiating, the pdf of Z becomes g ( z ) = exp(- z ) So Y and Z are also exponentially distributed, with parameters / 2 and 1, respectively. Example 2: Exponential distribution As before, X with pdf f X ( x ) = exp(- x ) , x > . Take Y = X 2 . What is the cdf of Y ? P ( Y < y ) = P ( X 2 < y ) = P ( X < y ) = 1- exp(- p ( y )) . The pdf becomes f Y ( y ) = exp(- y ) 2 y ....
View Full Document

This note was uploaded on 01/16/2011 for the course STAT 213 taught by Professor Ioannam during the Fall '09 term at Duke.

Page1 / 3

STA213lecture5.notes - Todays outline: pp 47-55 Examples of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online