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Unformatted text preview: ECE 804, Random Signal Analysis Oct. 4, 2010 OSU, Autumn 2010 Due: Oct. 11 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 different 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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