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Grinstead-Snell-Probability
· Problem 6.3.1
Sums of Random Variables
Mathematics · expected-value-variance-continuous
Problem
Let
X
X
X
be a random variable with range
[
−
1
,
1
]
[-1, 1]
[
−
1
,
1
]
and let
f
X
(
x
)
f_X(x)
f
X
(
x
)
be the density function of
X
X
X
. Find
μ
(
X
)
\mu(X)
μ
(
X
)
and
σ
2
(
X
)
\sigma^2(X)
σ
2
(
X
)
if, for
∣
x
∣
<
1
|x| < 1
∣
x
∣
<
1
, (a)
f
X
(
x
)
=
1
/
2
f_X(x) = 1/2
f
X
(
x
)
=
1/2
. (b)
f
X
(
x
)
=
∣
x
∣
f_X(x) = |x|
f
X
(
x
)
=
∣
x
∣
. (c)
f
X
(
x
)
=
1
−
∣
x
∣
f_X(x) = 1 - |x|
f
X
(
x
)
=
1
−
∣
x
∣
. (d)
f
X
(
x
)
=
(
3
/
2
)
x
2
f_X(x) = (3/2)x^2
f
X
(
x
)
=
(
3/2
)
x
2
.
Related theory
State Value And Action Value Functions
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