Unformatted text preview: X = 1, the 1 coming from the second toss being a heads preceeded by a heads. Find the mean and variance of X . Remark: indicator random variables can be helpful. 4 A point is picked at random from the unit disc. Let X be the distance of the point from the center of the disc, Y be the distance of the point from the edge of the disc, and Z be the quadrant the point is in, that is, Z = 1 if both X,Y are bigger than 0, Z = 2 if Y > 0, X < 0, Z = 3 if X,Y < 0, and Z = 4 if X > 0, Y < 0. Find EX , EXY , and EXY Z . 5 Let X k be continuous uniform on (0 ,k ), and let X i , i ≥ 1 be independent. Find P ( X n < X n1 < ··· < X 2 < X 1 )....
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 Spring '09
 Math, Probability theory, heads, Prof. B. Davis

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