Can you help me understand this PDF derivation please?

28 Views Asked by At

Can you help me understand this pdf derivation please? The part that I don't understand is when we differentiate $F_x(\frac{y - b} {a})$ by $dy$. Where does $\frac{1}{|a|}$ came from? How this differentiation happens?

1

There are 1 best solutions below

1
On BEST ANSWER

How this differentiation happens?

when you calculate the derivative of an integral function (that is your CDF) you get

$$\frac{d}{dx}\int_{-\infty}^{a(x)}f(t)dt=a'(x)f(a(x))$$

the absolute value is related to the fact that if $a(x)$ is increasing or decreasing the result does not change