# Thread: Joint distribution

1. ## Joint distribution

I am given X has distribution f(x)= (1/σ)*e^(-x/σ) and Y has the same distribution but with μ and y in place of sigma and x. I am also given Z=min{X,Y} and W={1 if Z=X and 0 if Z=Y}.
I am told to find the joint distribution of Z and W and also prove Z and W are independent.
I am stuck on this one. Does it break down into two cases (Z=X and Z=Y)?

2. Originally Posted by kman320
I am given X has distribution f(x)= (1/σ)*e^(-x/σ) and Y has the same distribution but with μ and y in place of sigma and x. I am also given Z=min{X,Y} and W={1 if Z=X and 0 if Z=Y}.
I am told to find the joint distribution of Z and W and also prove Z and W are independent.
I am stuck on this one. Does it break down into two cases (Z=X and Z=Y)?
kman320,

Are you sure of your problem statement? It looks to me like Z and W are dependent.

3. Its seems they are, but he gives a hint. Show the prob. that Z<z given W=i (for i=1,2) is equal to the prob. Z<z.
Show P(Z<z l W=i)=P(Z<z) .
How will I go about doing the first step of finding the joint dist. of Z & W?

4. Anyone?