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# hw1 - EE 278 Statistical Signal Processing Homework#1 Due...

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EE 278 September 23, 2009 Statistical Signal Processing Handout #1 Homework #1 Due: Wednesday September 30 You may either hand the assignment in class or drop it in the Homework In box in the EE 278 drawer of the class file cabinet on the second floor of the Packard Building by 5pm. Problems 1 and 2 are the bonus questions this week and you can bet up to 10 points on each question. 1. Monty Hall. (Bonus) Gold is placed behind one of three curtains. A contestant chooses one of the curtains. Monty Hall, the game host, opens an unselected empty curtain. The contestant can choose either to switch his selection to the third curtain or not. a. What is the sample space for this random experiment? Hint: an outcome consists of the curtain with gold, the curtain chosen by the contestant, and the curtain chosen by Monty. b. Assume that placement of the gold behind the three curtains is random, that the contestant’s choice of curtains is random and independent of the gold placement, and that Monty Hall’s choice of an empty curtain is equally likely between the two alternatives (if the two unselected curtains are empty). Specify the probability measure for this random experiment and use it to compute the probability of winning the gold if the contestant decides to switch. 2. Conditional coin toss. (Bonus) Let C 1 be an unbiased coin and let C 2 be a biased coin with probability of heads 3 / 4. C 1 is tossed at time t = 0. If the result is heads, then C 1 is tossed at time t

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hw1 - EE 278 Statistical Signal Processing Homework#1 Due...

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