A question related to Derived Distributions
Can anyoner help me to solve this question... I'm really stuck on this one :confused:
Andy is vacationing in Las Vegas. The amount X (in Dolars) he takes to casino each evening is a random variable
with a PDF of the form
fX(x)=ax if 0≤x≤23 and
At the end of each night, the amount Y that he has when leaving the casino is uniformly distributed between
zero and twice the amount that he came with.
Determine the joint PDF fX,Y(x,y).
What is the probability that on a given night Andy makes a positive profit at the casino?
Find the PDF of Andy's profit Z=Y-X on a particular night.
Determine the expected value of Z=Y-X.
Thank you very much.