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oldmidterm3 - UCSD ECE153 Handout #21 Prof. Young-Han Kim...

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Unformatted text preview: UCSD ECE153 Handout #21 Prof. Young-Han Kim Tuesday, May 3, 2011 Midterm Examination (Spring 2010) (Total: 120 points) There are 3 problems, each problem with 4 parts, each part worth 10 points. Your answer should be as clear and readable as possible. 1. Polyas 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....
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oldmidterm3 - UCSD ECE153 Handout #21 Prof. Young-Han Kim...

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