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Unformatted text preview: 4. Suppose that a voltage X is a zero-mean Gaussian random variable. Find the pdf of the power dissipated by an R-ohm resistor P = X 2 /R. 5. Let X be uniform on [-1,1]. Find g( x ) such that, if Y=g(X), then f Y ( y ) = 2e-2 y u( y ). 6. Let Y = e X . a. Find the cdf and pdf of Y in terms of the cdf and pdf of X. b. Find the pdf of Y when X is a Gaussian random variable. 7. Find the mean and variance of the binomial random variable. 8. Show that E[X] for the random variable with cdf 1 1/ 1 ( ) 1 X x x F x x-≥ & = ± < ² does not exist. 9. Let Y = Acos( & t )+c, where A is a random variable with mean m and variance ± 2 , and & and c are constants. Find the mean and variance of Y. 10. Let g(X) = ba X , where a and b are positive constants and X is a Poisson random variable. Find E[g(X)]....
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- Spring '08
- Probability theory, 1 K, CDF, Gaussian random variable