# Question

A random variable X has a characteristic function, ϕX (ω). Write the characteristic function of Y= aX+ b in terms of ϕX (ω) and the constants a and b.

## Answer to relevant Questions

Prove that the characteristic function of any random variable must satisfy the following properties. (a) ϕ*X (ω) = f X (– ω). (b) ϕX( 0) = 1. (c) For real ω, |f X (ω) = 1. (d) If the PDF is symmetric about the ...A Poisson random variable has a PMF of the form (a) Find the characteristic function,ϕX( ω ) . (b) Find the first three nonzero terms in the Taylor series expansion of ln[ϕX(ω)]. (c) Use the results of part (b) to find ...A certain random variable has a probability- generating function given by Find the PMF for this random variable. The current flowing through a 75 Ω resistor is modeled as a Gaussian random variable with parameters, m = 0A and σ = 15 mA . Find the average value of the power consumed in the resistor. The average number of cars per hour arriving at a toll booth is 57 while the standard deviation is 15. (a) Use Markov’s inequality to find an upper bound on the probability of having more than 200 cars arrive in an hour. ...Post your question

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