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# hw2 - UCSD ECE153 Prof Young-Han Kim Handout#9 Thursday...

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UCSD ECE153 Handout #9 Prof. Young-Han Kim Thursday, April 7, 2011 Homework Set #2 Due: Thursday, April 14, 2011 1. Polya’s urn. Suppose we have an urn containing one red ball and one blue ball. We draw a ball at random from the urn. If it is red, we put the drawn ball plus another red ball into the urn. If it is blue, we put the drawn ball plus another blue ball into the urn. We then repeat this process. At the n -th stage, we draw a ball at random from the urn with n + 1 balls, note its color, and put the drawn ball plus another ball of the same color into the urn. (a) Find the probability that the first ball is red. (b) Find the probability that the second ball is red. (c) Find the probability that the first three balls are all red. (d) Find the probability that two of the first three balls are red. 2. Uniform arrival. The arrival time of a professor to his office is uniformly distributed in the interval between 8 and 9 am. Find the probability that the professor will arrive during the next minute given that he has not arrived by 8:30. Repeat for 8:50.

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