Lec02.ParamEst

# Lec02.ParamEst - Regression Parameter Estimation KNNL Ch 1...

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Regression Parameter Estimation KNNL Ch. 1, Ch. 2

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Overview of Today’s Lecture Probability Density, cumulative distribution Expected Values Means, variances Least squares Parameter estimation, the linear model Maximum likelihood Example: Ping-pong
Binomial Probability Distribution dbinom(x,n,p) dbinom(5,10,0.5) 0.2460937 x n x p p x n p n x X P - - = = ) 1 ( ) , ; (

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Cumulative Binomial Probability Distribution pbinom(x,n,p) pbinom(5,10,0.5) 0.6230469 = - - = k x x n x p p x n p n k X P 0 ) 1 ( ) , ; (
Cumulative Binomial Probability Distribution pbinom(x,n,p) pbinom(10,10,0.5) 1 1 ) 1 ( ) , ; ( 0 = - = = - n x x n x p p x n p n n X P

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0 1 2 3 4 5 6 7 8 9 10 0.0 0.05 0.10 0.15 0.20 0.25 Number of Heads Probability x n x p p x n p n x X P - - = = ) 1 ( ) , ; (
Expected Value (Mean) x n x n x n x p p x n x p n x X P x X E - = = - = = = ) 1 ( ) , ; ( ) ( 0 0

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Expected Value (Mean) x n x n x x n x n x n x p p x n x n x p p x n x p n x X P x X E - = - = = - - = - = = = ) 1 ( )! ( ! ! ) 1 ( ) , ; ( ) ( 0 0 0
np p p x n x n np p p x n x n x p p x n x p n x X P x X E n x x n x x n x n x x n x n x n x = - - - - - - = - - = - = = = = - - - - - = - = = 1 ) 1 ( 1 1 0 0 0 ) 1 ( ))! 1 ( 1 ( )! 1 ( )! 1 ( ) 1 ( )! ( ! ! ) 1

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## This note was uploaded on 04/17/2010 for the course STSCI 3200 taught by Professor Sullivan during the Spring '10 term at Cornell.

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Lec02.ParamEst - Regression Parameter Estimation KNNL Ch 1...

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