Originally Posted by
feiyingx Let X and Y be independent random variables having the uniform density on {0, 1,..,N}. How do you find the density of min(X,Y)?
Here's what I did.
First i wrote out
P(min(X,Y) >= z) = P(X >= z, Y >= z)
= P(X >=z)*P(Y>=z)
= (N+1 - z + 1)/(N+1) * (N+1 - z + 1)/(N+1)
= (N+1-z+1)^2/(N+1)^2
I'm not whether that is the correct way to start. And I don't know what to do after that. The solution provided by the book is [2(N-z)+1]/(N+1)^2.
Can someone explain how to solve this problem?
Thanks!