5 4 suppose that x is a random variable that is

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Unformatted text preview: niformly distributed in [0, 1]. Define the new random variables Y = 3 X -1.5, Z = X5 and W = u(X - 0.2), where u is the unit-step function. a) Determine and plot the pdf of Y. b) Determine the pdf of Z. c) Determine and plot the cumulative distribution function of W. 6 5. A random variable Y has the cumulative distribution function shown below. It is known that P{Y=2}= 0.6. Plot the pdf of Y and calculate the FY(y) variance of Y. 1.0 0 y 2 6. Let N(t) represent the number of hits that a website receives in the interval [0,t], where t , in the units of minutes, is measured starting at 6 AM (namely, 6AM corresponds to t=0). Assume that N(t) is Poisson process with a mean arrival rate of 3 hits/minute. a) Find the correlation coefficient between N(2) and N(3). b) Give an example of another physical phenomenon that can be effectively modeled by a Poisson random variable or Poisson process. 7 7. A pair of random variables, X and Y, have a joint pdf given by fXY(x,y)=x+y, for 0≤x≤1, 0≤y≤1, and fXY(x,y)=0 otherwise. Calculate P{0 < X < 0.1 | Y=0.5}. Show all yo...
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This note was uploaded on 10/21/2012 for the course ECE 340 taught by Professor Calhoun,v during the Spring '08 term at New Mexico.

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