Probability Density Function

Creator

Creator

Created

Created

2023 Mar 7 2:31

Editor

Editor

Edited

Edited

2024 Dec 3 12:10

Refs

Refs

Random Variable

Cumulative Distribution Function

PDF

P(a\le X\le b) = \int_a^b f_X(x)dx \\ P(X\le x) = F_X(x)

can be greater than 1 at a particular point

Jacobian

The probability of the X interval is equal to the probability of the Y interval (thin rectangle area)

f_Y(y)dy = f_X(x)dx

For example

if

Y=X^2

,

f_X = \frac{dx}{dy}f_Y

and

dy = 2 xdx

. Therefore

f_Y = \frac{1}{2\sqrt{y}}

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