QUALIFYING EXAMINATION AUGUST 1999 MATH 519 - Prof. DasGupta (20) 1. The number of ﬁsh that Anirban catches on any given day has a poisson distribu-tion with mean 20. Due to the legendary softness of his heart, he sets free, on an average, 3 out of 4 ﬁsh he catches. Find the mean and the variance of the number of ﬁsh Anirban takes home on a given day. (20) 2. A fair die is rolled and at the same time a fair coin is tossed. This is done repeatedly. Find the probability that a head occurs (strictly) before a six occurs.
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