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## Sums of Continuous Random Variables

Definition: Convolution of two densitites:

Sums:For X and Y two random variables, and Z their sum, the density of Z is

Now if the random variables are independent, the density of their sum is the convolution of their densitites.

Examples:

1.
Sum of two independent uniform random variables:

Now fY(y)=1 only in [0,1]

This is zero unless ( ), otherwise it is zero: Case 1:
Case 2: , we have For z smaller than 0 or bigger than 2 the density is zero. This density is triangular.
2.
Density of two indendent exponentials with parameter . , for z>0

Susan Holmes
1998-12-07