This is some homework my professor assigned he said it should take roughly a half hour.

1. Let X be a Uniform(-8, 0) distribution. Consider the transformation: Y = X +0 20 Find the pdf of Y, using the "inverse transform" method. Also name the distribution of Y 2. Let Y be some ry (discrete or continuous). Let the transformation be: U = F(Y), where F(.) stands for the cdf. Find the pdf of U using the cdf method. Can you name the distribution of U? 3. Let X and Y be two discrete random variables with a common mgf of ell. After some analysis you conclude, X =4 and Y = 6. Is this a valid claim? Why or why not? 4. Let X1, X2 be independent random variables from N(un, of) and N(p2, of) distributions respectively. Find the pdf of Y = X1 - X2 using the mgf method