# Question: For the Rayleigh random variable described in Exercise 4 12 find

For the Rayleigh random variable described in Exercise 4.12, find a relationship between then th moment, E [Yn], and the n th moment of a standard normal random variable.

Find an expression for the even moments of a Rayleigh random variable. That is, find E [Y2m] for any positive integer m if the random variable, Y, has a PDF given by

Find an expression for the even moments of a Rayleigh random variable. That is, find E [Y2m] for any positive integer m if the random variable, Y, has a PDF given by

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Suppose X is a random variable whose n th moment is gn , n = 1,2, 3.… In terms of the gn, find an expression for the m th moment of the random variable Y= aX+ b for constants a and b . Prove that all odd central moments of a Gaussian random variable are equal to zero. Furthermore, develop an expression for all even central moments of a Gaussian random variable. Find the variance and coefficient of skewness for a geometric random variable whose PMF is You may want to use the results of Exercise 4.13. Suppose X is uniformly distributed over (– a, a), where a is some positive constant. Find the PDF of Y= X2. Let X be a Cauchy random variable whose PDF is given by Find the PDF of Y = 1 / X.Post your question