homework_10_2005

homework_10_2005 - Homework Set #10 Problem 1 Suppose that...

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Homework Set #10 Problem 1 Suppose that hurricanes occur according to a Poisson Point Process with unknown parameter λ . Given that 5 hurricanes occurred during a two-month period, estimate by: (a) The Method of Moments (b) The Method of Maximum Likelihood, and plot the Likelihood function [In this case, you should consider the random variable N = number of hurricanes in a two-month period. Notice that N has Poisson distribution with mean value 2 , where is in units of 1/month] Problem 2 Consider a random variable Y with probability density function: = otherwise 0, b y 0 , b y b ) y ( f Y 1 2 where b is an unknown parameter. ) y ( f Y 0 b b 2 Y
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The mean value of Y is b 3 1 m Y = . Given the following sample Y = { } 5 , 3 , 2 from the distribution of Y: (a) Estimate b by the method of moments . (b) Find and plot the likelihood function ) Y | b ( A (c) Find the maximum likelihood estimate of b and compare with the result from (a). Problem 3
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This note was uploaded on 12/04/2011 for the course ESD 1.151 taught by Professor Danieleveneziano during the Spring '05 term at MIT.

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homework_10_2005 - Homework Set #10 Problem 1 Suppose that...

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