aug29p - EXAM P QUESTIONS OF THE WEEK S. Broverman, 2005...

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EXAM P QUESTIONS OF THE WEEK S. Broverman, 2005 Question 6 - Week of August 29 \ ] Ö!ß "ß #× and are discrete random variables on the integers , with moment generating functions and . You are given the following: Q Ð>Ñ Q Ð>Ñ \] > ÑQÐ > Ñœ // > ÑQÐ > Ñœ / $$ " "" %% # ># > > and . Find . TÐ\ œ"Ñ A) B) C) D) E) ""$"& )%)#) The solution can be found below.
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Question 6 Solution We denote the probability function of by and \ : œTÐ\œ!Ñß: œTÐ\œ"Ñß !" \\ : œ TÐ\ œ #Ñ ] # \ . With similar notation for . Then and Q Ð>ÑœIÒ/ Óœ/ †: / †: / †: \ >\ ! \ > \ #> \ # ] >] ! ] > ] #> ] # . Then > ÑQÐ > Ñœ : / /† / : \] # # \> \# > \] > ] # > ] , œ: : Ð: : Ñ/ Ð: : Ñ/ !! "" ## > # > and it follows that
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aug29p - EXAM P QUESTIONS OF THE WEEK S. Broverman, 2005...

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