(a) Find the moment generating function of X and Y . (8%)
(b) Find the conditional expectation of X , given Y = y . (8%)
(c) Find the correlation coefficient between X and Y . (8%)
A coin, with a diameter of 2cm, is dropped into an empty can, whose round
bottom has a diameter of 10cm.
(a) What is the probability that the center of the can bottom is covered by
the coin? (5%)
(b) Assuming independence, how many coins would you have to drop to
have at least a 50% chance of covering the can bottom? (5%)
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