Let X and Y be i.i.d. Geom(p), L = min(X, Y ), and M = max(X, Y ). (a) Find the joint
Chapter 7, Problem 29(choose chapter or problem)
Let X and Y be i.i.d. Geom(p), L = min(X, Y ), and M = max(X, Y ). (a) Find the joint PMF of L and M. Are they independent? (b) Find the marginal distribution of L in two ways: using the joint PMF, and using a story. (c) Find EM. Hint: A quick way is to use (b) and the fact that L + M = X + Y . (d) Find the joint PMF of L and M L. Are they independent?
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