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Grinstead-Snell-Probability
· Problem 9.3.1
Generating Functions
Mathematics · central-limit-theorem-continuous
Problem
Let
X
X
X
be a continuous random variable with mean
μ
(
X
)
\mu(X)
μ
(
X
)
and variance
σ
2
(
X
)
\sigma^2(X)
σ
2
(
X
)
, and let
X
∗
=
(
X
−
μ
)
/
σ
X^* = (X - \mu)/\sigma
X
∗
=
(
X
−
μ
)
/
σ
be its standardized version. Verify directly that
μ
(
X
∗
)
=
0
\mu(X^*) = 0
μ
(
X
∗
)
=
0
and
σ
2
(
X
∗
)
=
1
\sigma^2(X^*) = 1
σ
2
(
X
∗
)
=
1
.
Related theory
Central Limit Theorem
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