I have a problem about deriving a pdf from a joint pdf:

Random variables x and y are described by the joint pdf:

f(x,y) = 0.5 if 0 <= y <= x <= 2

0.0 otherwise

random variable z is defined by: z=max(x,2y)

determine and sketch f(z), the probability density function (pdf) for random variable z

can anybody help with that?

I figured out that the range of z is between [0,2], otherwise it should out of the range of the original random variables.