W5-slides1 - Lecture 14- Outline and Examples Continuous...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 14- Outline and Examples Continuous random variables (Ross Ch 5) -Definition (Ross § 5.1) -Expected value and variance(Ross § 5.2) -Uniform random varibale (Ross § 5.3)
Background image of page 1

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

View Full DocumentRight Arrow Icon
Probability density functions Example Experience has shown that while walking in a certain park, the time X , in minutes, between seeing two people smoking has a density function of the form f ( x ) = ( λ xe - x x > 0 0 otherwise. (a) Calculate the value of λ . (b) Find the probability distribution function of X . (c) What is the probability that Jeff, who has just seen a person smoking, will see another person smoking in 2 to 5 minutes? In at least 7 minutes?
Background image of page 2
Expected value and Variance For discrete random variable X E [ X ] = X x xP ( X = x ) . The analogous definition when X is a continuous r.v. with p.d.f. f X is E [ X ] = R -∞ xf X ( x ) dx . As in the discrete case E [ g ( X )] = R -∞ g ( x ) f X ( x ) dx .
Background image of page 3

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

View Full DocumentRight Arrow Icon
Variance Var ( X ) = E [( X - μ ) 2 ] where μ = E [ X ]. Alternately, this can be written as Var ( X ) = E [ X 2 ] - ( E [ X ]) 2 .
Background image of page 4
Uniform random variables
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.

Page1 / 8

W5-slides1 - Lecture 14- Outline and Examples Continuous...

This preview shows document pages 1 - 8. Sign up to view the full document.

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