# Combination of Probability Density Functions

1. Dec 13, 2012

### FrankDrebon

Hi all,

I need to calculate the probability density function $f\left( Y \right)$ of a function $Y$ of two variables $A$ and $B$ with known individual probability density functions $f\left( A \right)$ and $f\left( B \right)$. What is the correct way to combine the PDF's?

Specifically, I have a variable Y dependent on A and B by:

$Y = A + 2B$

I know $f\left( A \right)$ and $f\left( B \right)$, how do I write $f\left( Y \right)$ in terms of $f\left( A \right)$ and $f\left( B \right)$?

Stats isn't my strong point so apologies if this is trivial!

F

2. Dec 13, 2012

### mathman

The most direct way is to do it in two steps.
Step 1: C = 2B (scale density function).
Step 2: Y = A + C (convolution of density functions of A and C results in density function for Y).