The pdf for an exponential distribution is exp (-x). To find the expectation we multiply by x and integrate to get 1/. To find the expectation of X^2 just square the pdf and multiply that by x and integrate. We get ( ^2)/4. Since X and Y are independent the expectation of the product is the product of the expectation. ie 1/4 (Note the subtlety X^2 IS dependent on X)

With uniform distribution this becomes a geometry problem. 2a is asking what portion of the square is covered by a circle of radius 1. 2b asks what portion of the square lies under the graph y=2x