ProbSetSix - Rensselaer Electrical, Computer, and Systems...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE 4500 Probability for Engineering Applications PS#6 Solutions March 29, 2010 1. (3.16) Let X n and X n +1 be two numbers generated in sequence by the random number gen- erator at the n th construct. Form Y n = X n + X n +1 .I fthe { X i } are generated independently, the pdf of Y n is f Y n ( y )= f X n ( y ) f X n +1 ( y ) and looks like So the form is right but the mean is wrong! Therefore generate Z n = Y n 1 .Th epd fo f Z n looks like Equivalently one could subtract 0 . 5 from X n and X n +1 before adding. In either case one can get f Z n ( z tri ( z/ 2) .H e r e t h e triangle function tri is de f ned as tri ( x ) , ½ 1 2 | x | , 1 2 <x< + 1 2 , 0 , else. 2. (3.17) We present a MATLAB function histonorm as follows: % The following program calculates the histogram of the no. % of "samples". Each sample is the sum of "sumrange" uniform % random numbers. Depending on the function call, the samples % are distributed in "n" evenly spaced bins containing the % minimum and maximum values of the samples. Thus empty bins % are not shown. Another function call will show all the bins % even the empty ones. "alpha" is a dummy variable.
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This note was uploaded on 04/15/2010 for the course ECSE 4500 taught by Professor Woods during the Spring '08 term at Rensselaer Polytechnic Institute.

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ProbSetSix - Rensselaer Electrical, Computer, and Systems...

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