This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ≤ 0. Also, the parameter λ is a positive real number. The exponential r.v. is often used as the distribution for the time required to complete a certain task or for the elapsed time between successive occurrences of a specified event. CDF: = ) ( x F X 0 for x ≤ 0. x X e x F − − = 1 ) ( for x > 0. Mean: 1 Variance: 2 1 λ Special Property 1: Memorylessness: If X is exponentially distributed, then its conditional probability obeys the following property: s t X P + > ( І X > s) = P(X > t) for all s, t ≥ 0. Example numbers: P(X>50 І X>35) = P(X > 15). Special Property 2: Tail Probability Function: If X is exponentially distributed, then we have a specific formula for X > x. x x X e e x F CDF x X P − − = − − = − = − = > ) 1 ( 1 ) ( 1 1 ) ( . Say X is exponentially distributed with lambda equal to 10. Then, P(X>50 І X>35) is 150 − e ....
View
Full
Document
This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue.
 Spring '08
 MARTIN

Click to edit the document details