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Unformatted text preview: and variance . 2 X ∼ ) , ( 2 N . Find the probability density function of Y . Clipped Rectifier 2 4. (a) The discrete r.v Z has the following probability mass function ( p.m.f ) ( 29 . 1 , , 2 , 1 , , ) 1 ( < < =-= = p k p p k Z P k Find the mean and variance of Z . (b) Find the mean and variance of a Rayleigh distributed r.v X ≥ =-. , , , ) ( 2 2 2 / 2 otherwise x e x x f x X σ 5. (a) Find the characteristic function of a Gamma r.v Z ). ( )! 1 ( ) ( / 1 z U e n z z f z n n Z β---= Here n is an integer. (b) Prove or disprove the following statements. (i) ( 29 ( 29 2 2 ) ( X E X E ≥ for any random variable X . (ii) The characteristic function of a r.v can be used to compute its central moments....
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- Spring '11
- Normal Distribution, Probability theory, Rayleigh, Characteristic function