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Reading 10b: Maximum Likelihood Estimates

Maximum Likelihood EstimatesClass 10, Orloff and Jonathan Bloom1 Learning Goals1. Be able to define the Likelihood function for a parametric model given Be able to compute the Maximum Likelihood estimate of unknown parameter(s).2 IntroductionSuppose we know we have data consisting of valuesx1,..,xndrawn from an exponentialdistribution. The question remains: which exponential distribution?!We have casually referred totheexponential distribution orthebinomial distribution orthenormal distribution. In fact the exponential distribution exp( ) is not a single distributionbut rather a one-parameter family of distributions.

De nition: Given data the maximum likelihood estimate (MLE) for the parameter pis the value of pthat maximizes the likelihood P(data jp). That is, the MLE is the value of pfor which the data is most likely. answer: For the problem at hand, we saw above that the likelihood 100

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