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Values - Generalised Linear Models - Exam

Exams, Mathematics

Post: February 27th, 2013
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This is the Past Exam of Generalised Linear Models which includes Values, Fixed, Integer, Expectation, Variance, Probability Mass Function, Standard Notation, Logit Functions, Logistic etc. Key important points are: Values, Fixed, Integer, Expectation, Variance, Probability Mass Function, Standard Notation, Logit Functions, Logistic, Residual Deviance
This is the Past Exam of Generalised Linear Models which includes Values, Fixed, Integer, Expectation, Variance, Probability Mass Function, Standard Notation, Logit Functions, Logistic etc. Key important points are: Values, Fixed, Integer, Expectation, Variance, Probability Mass Function, Standard Notation, Logit Functions, Logistic, Residual Deviance
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LANCASTER UNIVERSITY 2007 EXAMINATIONS PART II (Third or Fourth Year) MATHEMATICS & STATISTICS Math 352 Generalised Linear Models 90 minutes You should answer ALL Section A questions and ONE Section B question. In Section A there are questions worth a total of 50 marks, but the maximum mark that you can gain there is capped at 40. SECTION A A1. Let Z ∼ Bino(m, µ), 0 < µ < 1, and fixed known integer m > 0. Define Y = Z/m so that Y ∼ Binoprop(m, µ). (a) State the values of Z (the support) which have non-zero probability. (b) Find the expectation and variance Y . (c) Write down the probability mass function of Y . (d) Explain why Z is not a GLM in the standard notation of GLMs but that Y is. A2. Define the logistic and logit functions, and show these are inverse. A3. Define the residual deviance of a GLM in terms of the log likelihood, expressed as a function of the moment parameters, µi , and the observations, yi , i = 1, 2, . . . , n. State what the deviance measures. A4. S..

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