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Grinstead-Snell-Probability
· Problem 6.3.7
Sums of Random Variables
Mathematics · expected-value-variance-continuous
Problem
Let
X
X
X
be a random variable with density function
f
X
f_X
f
X
. Show, using elementary calculus, that the function
ϕ
(
a
)
=
E
(
(
X
−
a
)
2
)
\phi(a) = E((X - a)^2)
ϕ
(
a
)
=
E
((
X
−
a
)
2
)
takes its minimum value when
a
=
μ
(
X
)
a = \mu(X)
a
=
μ
(
X
)
, and in that case
ϕ
(
a
)
=
σ
2
(
X
)
\phi(a) = \sigma^2(X)
ϕ
(
a
)
=
σ
2
(
X
)
.
Related theory
State Value And Action Value Functions
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