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**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!