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Beta Function
3.1
𝖯
(
X
=
x
)
=
F
X
(
x
)
-
lim
i
→
∞
F
X
(
x
-
1
/
i
)
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Appendix C
Proofs of additional results
This material is included for completeness; it is beyond the scope of Math230 and is non-examinable.
3.1
𝖯
(
X
=
x
)
=
F
X
(
x
)
-
lim
i
→
∞
F
X
(
x
-
1
/
i
)
3.2
The Law of the Unconscious Statistician
3.3
Odd central moments of symmetric distributions
3.4
The formula for a bivariate change of variable
3.5
Formal proof of the CLT