hwset1 - EE 278 Handout #2 Statistical Signal Processing...

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Unformatted text preview: EE 278 Handout #2 Statistical Signal Processing Monday, June 29, 2009 Homework Set #1 Due: Monday, July 6, 2004. Announcement: The homework is due next Monday. You can either hand it in after class or deposit it, before 5pm, in the Homework in box in the 278 drawer of the class file cabinet on the second floor of the Packard Building. 1. Monty Hall Gold is placed behind one of three curtains. A contestant chooses one of the curtains. Monty Hall, the game host, opens one of the two unselected empty curtains. The contestant has a choice 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 random among the two alternatives. 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. Geometric pairs Consider a probability space consisting of the sample space Ω = { 1 , 2 , 3 ,... } 2 = { ( k,m ) : k,m ∈ Z + } , i.e., all pairs of positive integers, where the set of events is the power set of Ω and the probability measure on points in the sample space is P(( k,m )) = p 2 (1- p ) k + m- 2 for 0 < p < 1 . (a) Find P( { ( k,m ) : k ≥ m } ). (b) Find P( { ( k,m ) : k + m = r } ) as a function of r for r = 2 , 3 , 4 ,... ....
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This note was uploaded on 10/26/2011 for the course ECE 180 taught by Professor Eggers during the Spring '11 term at Aarhus Universitet.

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hwset1 - EE 278 Handout #2 Statistical Signal Processing...

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