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Unformatted text preview: EE 278 September 30, 2009 Statistical Signal Processing Handout #2 Homework #2 Due: Wednesday October 7 1. Probabilities from cdf. The cdf of random variable X is given by F X ( x ) = braceleftBigg 1 3 + 2 3 ( x + 1) 2 1 x x < 1 a. Find the probabilities of the following events. A = { X > 1 3 } , B = { X  1 } , C = { X 1 3  < 1 } , D = { X < } . b. Does X have a pdf? Explain your answer. 2. Distance to nearest star. (Bonus) Let the random variable N be the number of stars in a region of space of volume V . Assume that N is a Poisson random variable with pmf p N ( n ) = e V ( V ) n n ! , n = 0 , 1 , 2 ,..., where is the density of stars in space. We choose an arbitrary point in space and define the random variable X to be the distance from the chosen point to the nearest star. Find the pdf of X in terms . 3. Additive Gaussian noise channel. A communication channel has a realvalued input signal X and an output Y = X + 2 Z , where Z N (0 , . 09). Suppose that X = 1 is sent. Use the attached table of the Q ( ) function to find the probability of the event { Y > } . 4. Lognormal pdf. Let X N (0 , 2 ). Find the pdf of Y = e X ....
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This note was uploaded on 11/28/2009 for the course EE 278 taught by Professor Balajiprabhakar during the Fall '09 term at Stanford.
 Fall '09
 BalajiPrabhakar
 Signal Processing

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