quiz2solutions

quiz2solutions - STAT 231 Spring 2009 Assignment 1 This...

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Unformatted text preview: STAT 231 Spring 2009 - Assignment 1 This assignment is out of 33 marks, each mark is denoted by [1] in the following mark scheme. Please mark in RED INK and give a brief indication to the student of why you have taken off marks when you do. The solutions are in BOLD, everything else was on the question sheet. Please put your initials on top of each solution you mark so that we can trace back if the student has questions. 1. Consider Model ( ?? ). You may assume that n P = 50 is large enough for the Gaussian approximation to the Binomial to hold and that ∑ 50 i =1 s i = 10. (a) [3 marks] Write down the log-likelihood function for π in terms of the data s i ,i = 1 ,. .. , 50. The likelihood is Q 50 i =1 π s i (1- π ) 1- s i [1] for prod, [1] for limits, [1] for pdf. Do not deduce if n P is used instead of 50 , or if correct simplifications are made. (b) [4 marks] If the maximum likelihood estimate b π equals ∑ 50 i =1 s i / 50 = 1 / 5, write down the estimator e π and show that its mean value is...
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quiz2solutions - STAT 231 Spring 2009 Assignment 1 This...

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