HEII - University of Illinois Fall 2009 ECE 313: Hour Exam...

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University of Illinois Fall 2009 ECE 313: Hour Exam II Monday November 16, 2009 7:00 p.m. — 8:00 p.m. 100 Materials Science and Engineering Building 1. [15 points] Messages can be transmitted between Champaign-Urbana and Springfield either directly or via Decatur on communication links whose capacities are indicated on the diagram shown below. Assume that the three links fail independently with equal probability 1 2 . Let X denote the communication capacity between Champaign-Urbana and Springfield. 40 Springfeld Champaign-Urbana Decatur 200 100 (a) [5 points] What values can X take on? (b) [10 points] Find the expected value of X . 2. [10 points] Let X denote a Gaussian random variable with mean 2 and variance 25. Use the table of values of the unit Gaussian CDF Φ( · ) on the last page of this exam booklet to find the numerical value of P {| X - 4 | > 3 } . 3. [15 points] Let X denote a continuous random variable with zero mean and variance 1, that is, E [ X ] = 0 and var ( X ) = 1.
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HEII - University of Illinois Fall 2009 ECE 313: Hour Exam...

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