Suppose X is an integer- valued random variable. Show that in this case, ϕX( 2πn) = 1 for any integer, n . Likewise, prove the reverse is also true. That is, show that if ϕX( 2πn) = 1 for any integer, n , the random variable X must be integer- valued.
Answer to relevant QuestionsFor a Laplace random variable Whose PDF is given by Find the following: (a) The characteristic function, ϕ X (ω), (b) The Taylor series expansion of ϕX (ω), (c) A general expression for the k th moment of X. Which of the following functions could be the characteristic function of a random variable? See Appendix E, Section 5 for definitions of these functions. (a) f a( ω) = rect( ω ). (b) f b( ω) = tri( ω). (c) f c( ω) = ...Suppose HX( z) is the probability- generating function of some random variable X with PMF PX( k) . In terms of PX( k) , find the PMF of the random variable Y if its probability- generating function is given as in each of the ...Find the mean of the random variable whose moment- generating function is The received voltage in a 75 Ω antenna of a wireless communication system is modeled as a Rayleigh random variable, What does the value of the parameter σ need to be for the received power to be 10µW ?
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