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# ps2 - ECE 804 Random Signal Analysis OSU Autumn 2008 Oct 6...

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ECE 804, Random Signal Analysis Oct. 6, 2008 OSU, Autumn 2008 Due: Oct. 13, 2008 Problem Set 2 Problem 1 Let X 1 , . . . , X n be a sequence of numbers, where each number takes on the value 0 , 1 or 2 with probability 1 2 , 1 4 and 1 4 respectively. (a) What is the total number of all possible sequences? (b) Let us call two sequences ‘identical’ if they contain identical number of zeros, ones and twos. What is the total number of ‘distinct’ sequences? (c) What is the probability that a given sequence contains exactly n 2 zeros? (d) Let n = 3. Calculate P (number of twos = 2 | X 1 + X 2 + X 3 = 4). Problem 2 Two players A and B are playing the following game. There is an urn containing 4 red, 3 yellow and 2 white balls. First, player A draws three balls without replacement and wins the game if the balls she draws have three di±erent colors. Otherwise, she puts the balls back and B repeats the same with the same condition of winning. They keep going until there is a winner.

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ps2 - ECE 804 Random Signal Analysis OSU Autumn 2008 Oct 6...

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