ps07 - University of Illinois Spring 2010 ECE 313: Problem...

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University of Illinois Spring 2010 ECE 313: Problem Set 7 Decision Making; Independent Events; System Reliability Due: Wednesday March 10 at 4 p.m. Reading: Ross, Chapter 3; PowerPoint Lecture Slides 15-19 Noncredit Exercises: Chapter 3: Problems 53, 58, 59, 62, 63, 70-74, 78, 81 Theoretical Exercises 6, 7(a), 25, 26; Self-Test Problems 15-26. This Problem Set contains seven problems. 1. [ Mutually exclusive events ] Let A and B denote two mutually exclusive events that can occur on a trial of an experiment. Repeated independent trials of the experiment are carried out until either the event A or the event B occurs. What is the probability that A occurs before B does? (See Example 4h in Chapter 3 of Ross) 2. [ Detection problem with geometric distribution vs. Poisson distribution ] Consider a detection problem with the following two hypotheses for an observation X: H 0 : X has the Poisson distribution with parameter λ = 10: H 1 : X has the geometric distribution with parameter p = 0:1: (a) To get some intuition about this problem, calculate the mean, variance, and standard deviation of X under H 0 and under H 1 : (b) Describe the ML decision rule. Express it as directly in terms of X as possible. (c) Describe the MAP decision rule, under the assumption that H 0 is a priori 5 times more likely than H 1 (i.e, π 0 / π 1 = 5): Express the rule as directly in terms of X as possible. 3. [
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ps07 - University of Illinois Spring 2010 ECE 313: Problem...

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