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Grinstead-Snell-Probability
· Problem 10.3.7
Markov Chains
Mathematics · moment-generating-functions-continuous
Problem
Let
X
X
X
be a continuous random variable with values in
[
0
,
1
]
[0, 1]
[
0
,
1
]
, uniform density function
f
X
(
x
)
≡
1
f_X(x) \equiv 1
f
X
(
x
)
≡
1
and moment generating function
g
(
t
)
=
(
e
t
−
1
)
/
t
g(t) = (e^t - 1)/t
g
(
t
)
=
(
e
t
−
1
)
/
t
. Find in terms of
g
(
t
)
g(t)
g
(
t
)
the moment generating function for (a)
−
X
-X
−
X
. (b)
1
+
X
1 + X
1
+
X
. (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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