Question

To each part of the homework problems, make a complete problem statement and then show your work for each solution with detailed steps, otherwise, your solution will receive a grade zero, even if it is correct.

  

Suppose you are told that independent random variables X and Y each have a uniform density on {1,2,…,N}.

1. List explicitly, in terms of N, the elements (x,y) of (X,Y) and then, write down the joint density function density Pr (X=x, Y=y)

2. List the elements in the event A={(x,y)|X>Y} and again in terms of N, how many elements are in A? Then find Pr (A)

3. Find Pr (X=Y) in terms of N. Explain! If U=min (X,Y) find in terms of N the expression for the density function Pr (U=1) (Hint: First list the elements) same for Pr (U=2).

4. Well now write Pr (U=k) for arbitrary integer k, given 0<k<N+1

Answer 1