chap5slides

chap5slides - Chapter 5 Introduction to Random Variables...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 5 Introduction to Random Variables ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Random Variables Introduction In many random experiments: We are interested in numerical quantities derived from the experimental outcomes, or It is convenient to assign numerical labels to outcomes. ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 2
Background image of page 2
Random Variables Introduction Example Experiment: A fair coin is flipped twice. Sample space: S = { HH,HT,TH,TT } Events algebra: F = P S = {∅ , { HH } ,...,S } We are interested in the number of tails ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
Random Variables Introduction Example Assigning labels S HH HT TH TT 0 1 2 R ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 4
Background image of page 4
Random Variables Introduction Example Experiment: Pick a car out of a black Escort ( Eb ), a red Escort ( Er ) and a yellow Mazda ( My ). Sample space: S = { Eb,Er,My } Events algebra: F = P S We are only interested in the make of the car not the color. ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 5
Background image of page 5

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

View Full DocumentRight Arrow Icon
Random Variables Introduction Example Assigning labels S Eb Er My 0 1 R ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 6
Background image of page 6
Random Variables Introduction Mathematically speaking. .. Sample space: S . We define a function from S into R X : s S X ( s ) R . ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 7
Background image of page 7

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

View Full DocumentRight Arrow Icon
Random Variables Definition Definition Let ( S, F ,P ) be a probability space. A function X : s S X ( s ) R is called a random variable (RV) if for all x R : { s S : X ( s ) x } ∈ F . ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 8
Background image of page 8
Random Variables Introduction S s 1 s 2 s 3 s 4 s n X ( s 1 ) X ( s 2 ) X ( s 3 ) X ( s 4 ) = X ( s n ) R Domain of X ( · ) Range of X ( · ) : R X = { X ( s ) : s S } ECSE 305 - Winter 2012 (slides based on the notes by B. Champagne) 9
Background image of page 9

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

View Full DocumentRight Arrow Icon
Random Variables Remarks The function X ( · ) is called a Random Variable (RV), because: The value X ( s ) depends on the outcome s . The outcome s is unknown beforehand, and so is X ( s ) . Each experimental trial may lead to a different value of X ( s ) .
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 38

chap5slides - Chapter 5 Introduction to Random Variables...

This preview shows document pages 1 - 11. Sign up to view the full document.

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