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# PS11 - University of Illinois Fall 2009 ECE 313 Problem Set...

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Unformatted text preview: University of Illinois Fall 2009 ECE 313: Problem Set 11 Poisson Processes; Function of a Random Variable; Decision-Making Due: Wednesday November 11 at 4 p.m. Reading: Ross, Chapter 5; Powerpoint Lecture Slides, Sets 25-29 Noncredit Exercises: Chapter 5: Problems 37-41; Theoretical Exercises 18-21, 29, 30; Self-Test Problems 14, 16, 20 1. [Conditional Probabilities in a Poisson Process] Consider a Poisson process with arrival rate λ . Given that M packets arrived in (0 ,t ], what is the conditional probability that exactly k packets arrived in (0 ,τ ], where τ < t and 0 ≤ k ≤ M ? That is, find P { N (0 ,τ ] = k | N (0 ,t ] = M } . 2. [Random chords] It might help to read Example 3d in Chapter 5 of Ross before working this problem. Let the straight line segment ACB be a diameter of a circle of unit radius and center C. Consider an arc AD of the circle where the length X of the arc (measured clockwise around the circle) is a random variable uniformly distributed on [0, 2 π ). Now consider the random chord AD whose length we denote)....
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PS11 - University of Illinois Fall 2009 ECE 313 Problem Set...

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