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

1. For z<0 or z>2 : find fZ(z)
2. For 0≤z≤1 : find fZ(z)

Answer 1

1. 0
2. 2*z

3. For 1≤z≤2 : find fZ(z)?

Answer 2

3. 0.5

Answer 3

1. 0
2. z
3. 1/2