Let X and Y be independently random variables, with X uniformly distributed on [0,1] and Y uniformly distributed on [0,2] . Find the PDF fZ(z) of Z=max{X,Y} .

Question

For z<0 or z>2 :

fZ(z)=

For 0≤z≤1 :

fZ(z)=

For 1≤z≤2 :

fZ(z)=

Answer 1

a. 0
b. 1/4
c. 3/4