Find Probability Density Function of Z=X+Y

[grunkypeep]

Suppose X and Y are both uniform random variables on [0, 1] and they are independent. What is the probability density function of Z = X + Y ?

I understand that to find the PDF, I need to calculate the CDF and differentiate with respect to z. What I don't understand is how to find the CDF for this problem. Any help is greatly appreciated.

 

[Steven G]

What are you having trouble with finding the CDF? Why is it different to you than other similar problems?

 

[Romsek]

The density of the sum of two independent random variables is the convolution of their individual densities.
This is particularly simple in this problem yielding (which I leave you to show) that

\(\displaystyle f_Z(z) = 1-|z-1|,~z \in [0,2]\)