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Grinstead-Snell-Probability
· Problem 10.1.7
Generating Functions
Mathematics · generating-functions-discrete
Problem
Let
X
X
X
be a discrete random variable with values in
{
0
,
1
,
2
,
…
,
n
}
\{0, 1, 2, \ldots, n\}
{
0
,
1
,
2
,
…
,
n
}
and moment generating function
g
(
t
)
g(t)
g
(
t
)
. Find, in terms of
g
(
t
)
g(t)
g
(
t
)
, the generating functions for (a)
−
X
-X
−
X
. (b)
X
+
1
X + 1
X
+
1
. (c)
3
X
3X
3
X
. (d)
a
X
+
b
aX + b
a
X
+
b
.
Related theory
Characteristic Functions And Moment Generating Functions
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