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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 NX~Poisson(mu.(1p)) 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.
 Fall '08
 Chisholm
 Probability

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