Summing Uniform Distributions

[infinity_zero]

Hi, I can't seem to work out (or find anywhere) how to add two independent uniform distributions.

My problem is as follows:

I have random variable X~Unif(0,13), and error Z~Unif(-0.5,0.5) which is independent of X.
I need to find Y=X+Z, the joint pdf of X and Y, as well as the correlation coefficient.

Thanks in advance for any help.

 

[BGM]

1) Standard Jacobian Transformation technique.

2) For the correlation coefficients you do not even need the joint pdf.

Please show your effort for these kinds of homework problem, according to TS policy. Thanks.