I am currently working on an old exam for practice for my final. The question I am having trouble with is this.
"Suppose that X~Exponential(mean=1) and Y~Uniform[0,3] are independent continuous random variables. Compute Pr(X+Y<=2)?"
I know how to compute the sum of two independent random variables that have the same distribution, but not if they have different distributions. Do I have to use the convolution formula? or can I just assume that because they are independent I do find the probability of each distribution when they are equal to or less than two? or can I use some manipulation of Bayes' theorem?