H2 - Statistical Pattern Recognition University of...

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Unformatted text preview: Statistical Pattern Recognition University of Maryland, College Park September 15, 2009 Professor Rama Chellappa Handout 2 Homework 2 This problem set is due Tuesday September 22 at 11:00AM . 1. In a heads or tails coin tossing experiment the probability of occurrence of the head (1) is q and that of a tail (0) is 1- q . Let x i , i = 1 , 2 , . . ., N , be the resulting experimental outcomes, x i { , 1 } . Show that the ML estimate of q is q ML = 1 N N summationdisplay i =1 x i Hint: The likelihood function is P ( X : q ) = N productdisplay i =1 q x i (1- q ) 1- x i Then show that the ML results from the solution of the equation q i x i (1- q ) ( N- i x i ) parenleftbigg i x i q- N- i x i 1- q parenrightbigg = 0 2. In classroom it was shown that the ML estimate of the unknowns mean and covari- ance matrix of a Gaussian likelihood function are given by = 1 N N summationdisplay k =1 x k = 1 N N summationdisplay k =1 ( x k- )( x k- ) T Prove that the ML estimates of the mean and the covariance matrix can be computed...
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H2 - Statistical Pattern Recognition University of...

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