STAT 333 tutorial4 - with answers

STAT 333 tutorial4 - with answers - Tutorial 4 - Jiheng -...

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Unformatted text preview: Tutorial 4 - Jiheng - June 4 1 of 2 https://uwangel.uwaterloo.ca/uwangel/Section/Content/Page.aspx?EntryI... These problems will give you some practice using pgfs (and generating functions in general) 1. If X and Y are geometrically distributed with parameter p and independent of each other, find the probability mass function of X+Y. 2. Suppose that given N = n, X has binomial distribution with parameters n and p. Suppose also N has Poisson distribution with parameter mu. Use the technique of generating functions to find: (a) the marginal distribution of X. (b) the distribution of N - X. a- so X~Poisson(mu.p) b- so N-X~Poisson(mu.(1-p)) 3. Give the sequences generated by the following: a) A(s) = (s2 - s - 12)-1 b) B(s) = s/(5 + 3s) c) C(s) = (-3 + 2s)/(s2 - 3s - 4) a- b- c- 4. Let {an} be a sequence with generating function A(s), |s| < R, R > 0. Find the generating functions of a) {c + an} where c is a real number 12/10/2011 7:36 AM Tutorial 4 - Jiheng - June 4 2 of 2 https://uwangel.uwaterloo.ca/uwangel/Section/Content/Page.aspx?EntryI... b) {can} where c is a real number c) {an+an+2} d) {(n + 1)an} a- where R is the radius of convergence for A(s) b- c- d- 12/10/2011 7:36 AM ...
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This note was uploaded on 01/21/2012 for the course STAT 333 taught by Professor Chisholm during the Fall '08 term at Waterloo.

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