# lec8 - Statistics of R.V.s Expectation The expected value...

This preview shows pages 1–4. Sign up to view the full content.

Statistics of R.V.s Expectation The expected value of a function h ( X ) is deFned as E [ h ( X )] := i h ( x i ) · p X ( x i ) . The most important version of this is the case h ( x ) = x : E [ X ] = i x i · p X ( x i ) =: μ E [ X ] is usually denoted by the symbol μ . The expected value of a random variable E [ X ] is a measure of the average value of the possible values of the random variable. We see that it is actually a weighted average of the values of X , weighted by the point masses p X 1

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

View Full Document
Example Toss a Die Toss a fair die, and denote by X the number of spots on the upturned face. What is the expected value for X ? The probability mass function of X is p X ( i ) = 1 6 for all i ∈ { 1 , 2 , 3 , 4 , 5 , 6 } . Therefore, using the deFnition E [ X ] = 6 s i =1 ip X ( i ) = 1 · 1 6 + 2 · 1 6 + 3 · 1 6 + 4 · 1 6 + 5 · 1 6 + 6 · 1 6 = 3 . 5 . This formula shows that E ( X ) is also the center of gravity of masses p X placed at corresponding points x . 2
Statistics of R.V.s Variance A second common measure for describing a random variable is a measure of how far its values are spread out. The variance of a random variable X is deFned as: V ar [ X ] := E [( X E [ X ]) 2 ] = i ( x i E [ X ]) 2 · p X ( x i ) V ar [ X ] is usually denoted by the symbol σ 2 The variance is measured in squared units of 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 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.

### Page1 / 12

lec8 - Statistics of R.V.s Expectation The expected value...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online