# JMF-4-07 - Discrete Random Variables Chapter 4 Notes Set 4...

This preview shows pages 1–12. Sign up to view the full content.

CH Reilly UCF - IEMS - STA 3032 1 Discrete Random Variables Chapter 4 Notes Set 4 Spring 2007

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

View Full Document
CH Reilly UCF - IEMS - STA 3032 2 Random variable A random variable is a function that assigns an (unknown) numerical value from a sample space to each possible outcome or trial. Discrete random variable (Chapter 4) – countable number of possible values. Continuous random variable (Chapter 5) – uncountable number of possible values. The probability distribution for a random variable may be represented in functional, tabular, or graphical form.
CH Reilly UCF - IEMS - STA 3032 3 Probability distribution X is a random variable whose realized value is denoted by x . (Other letters, besides X and x , will sometimes be used to represent random variables and their values.) The probability distribution of X tells us f(x)= Pr (X=x) for all possible values x of X .

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

View Full Document
CH Reilly UCF - IEMS - STA 3032 4 Probability distribution (cont’d.) y.) probabilit of rules the (Recall 1 ) ( outcome.) simple a is ( . , 0 ) Pr( ) ( all = 2200 = = x x f x x x X x f
CH Reilly UCF - IEMS - STA 3032 5 Probability distribution (cont’d.) There are a number of ways to represent a probability distribution for a discrete random variable graphically, including: Probability histogram – total area is 1 square unit. Probability bar chart – heights of “pegs” represent the probabilities for each possible value. Sometimes the probability distribution function for a discrete random variable is called a probability mass function (pmf).

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

View Full Document
CH Reilly UCF - IEMS - STA 3032 6 Cumulative distribution function F(x) = Pr( X x ) for all possible values x of X . The cumulative distribution function is often referred to as a cdf for convenience; sometimes it is simply called a distribution function. Note that differences in cdf values can be used to find probabilities for particular values of X .
CH Reilly UCF - IEMS - STA 3032 7 Expected value of a random variable The expected value of a random variable is the mean value of the random variable. Expected values are population parameters. Expected values are sometimes called expectations. (I use the terms interchangeably.) The expectation of a random variable is not necessarily one of the possible values of the random variable.

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

View Full Document
CH Reilly UCF - IEMS - STA 3032 8 Expected value (cont’d.) = = = = x x x x f x X x f x g X g x f x X all 2 2 all all ) ( ) ( E ) ( ) ( )) ( ( E ) ( ) ( E μ
CH Reilly UCF - IEMS - STA 3032 9 Variance of X ( 29 ( 29 ( 29 2 2 2 2 2 2 2 ) ( E ) ( E ) ( E E ) ( Var σ μ + = - = - = - = = X X X X X

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

View Full Document
CH Reilly UCF - IEMS - STA 3032 10 Example x 1 3 4 6 f(x) 0.10 0.20 0.40 0.30 F(x) 0.10 0.30 0.70 1.00
CH Reilly UCF - IEMS - STA 3032 11 Example (cont’d.) ( 29 5133 . 1 29 . 2 ) 1 . 4 ( 1 . 19 ) ( E ) ( E 1 . 19 ) 30 . 0 )( 6 ( ) 10 . 0 )( 1 ( ) ( E 1 . 4 ) 30 . 0 )( 6 ( ) 10 . 0 )( 1 ( ) ( E 2 2 2 2 2 2 2 = - = - = = + + = = + + = = σ μ X X X X

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/22/2010 for the course STA 3032 taught by Professor Sapkota during the Spring '08 term at University of Central Florida.

### Page1 / 45

JMF-4-07 - Discrete Random Variables Chapter 4 Notes Set 4...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online