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Change-of-variables formula for a probability density
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Area of mathematics
Probability and statistics
Probability theory
Probability distribution
Continuous probability distribution
Probability density function
2026-09-28
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If
Y
=
g
(
X
)
for
a
differentiable
bijection
, then
f
Y
(
y
)
=
f
X
(
g
−
1
(
y
))
det
D
g
−
1
(
y
)
.
(1)
This is the
change of variables formula
applied to
probability density
.
Ancestors
(8)
Probability density function
Continuous probability distribution
Probability distribution
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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(3)
Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 320
/
1
/
c
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 218
/
3
/
d
/
Solution
Random-orientation distribution of an apparent oblate axis ratio
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