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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
\]
QÐ
>
ÑQÐ
>
Ñœ //
>
ÑQÐ
>
Ñœ /
$$
"
""
%%
#
>#
>
>
and
.
Find
.
TÐ\ œ"Ñ
A)
B)
C)
D)
E)
""$"&
)%)#)
The solution can be found below.
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View Full DocumentQuestion 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
QÐ
>
ÑQÐ
>
Ñœ
:
/
†
/†
/
†
:
\]
#
#
\>
\#
>
\] >
] #
>
]
,
œ: : Ð: : Ñ/ Ð: : Ñ/
!!
""
##
>
#
>
and it follows that
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 Spring '10
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