Problem 1 say we have a discrete rv X with pmf f(x)=c/log(x), x=2,3, ..,10. Find c. Say Y = X mod 4. Find the pmf of Y.
Problem 2 say X is a double exponential rv, ie it has density f(x)=½exp(-|x|). Let Y=round(|X|), that is the absolute value of X rounded to the nearest integer. Find EY. Verify your answer using R. Is the answer the same as E|X|?
Problem 3 say (X,Y) is a rv with joint density f(x,y)=6x, 0<x<y<1, 0 otherwise. Let U=X2 and V=XY. Find the joint pdf of (U,V). Verify that your answer is indeed a pdf.