{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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 Document Right 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 Document Right 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 Document Right 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 Document Right Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

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 bookmark
Ask a homework question - tutors are online