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STAT 333 tutorial4

# STAT 333 tutorial4 - X(b the distribution of N-X 3 Give the...

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Stat 333 - Tutorial 4 These problems will give you some practice using p.g.f.’s (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 . Sup- pose also N has Poisson distribution with parameter μ . Use the technique of generating functions to ﬁnd: (a) the marginal distribution of
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Unformatted text preview: X . (b) the distribution of N-X . 3. Give the sequences generated by the following: (a) A ( s ) = ( s 2-s-12)-1 (b) B ( s ) = s 5+3 s (c) C ( s ) =-3+2 s s 2-3 s-4 4. 4. Let { a n } be a sequence with generating function A ( s ) , | s | < R , R > . Find the generating functions of (a) { c + a n } where c is a real number. (b) ca n where c is a real number. (c) { a n + a n +2 } . (d) ( n + 1) a n . 1...
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