# Question

In this problem, we generalize the results of Exercise. Suppose a discrete random variable takes on nonnegative integer values and has a CDF of the general form

(a)What conditions must the sequence ak satisfy for this to be a valid CDF.

(b) For a positive integer n, find Pr (X ≤ n) in terms of the ak.

(a)What conditions must the sequence ak satisfy for this to be a valid CDF.

(b) For a positive integer n, find Pr (X ≤ n) in terms of the ak.

## Answer to relevant Questions

A random variable has a CDF given by Fx (x) = (1 –e –z) u (x). (a) Find Pr (X > 3). (b) Find Pr (X < 5| X > 3). (c) Find Pr (X > 6 | X > 3). (d) Find Pr (|X –5| < 4||X –6| > 2). The amplitude, A, of a received signal in a wireless communication system is often modelled as a Rayleigh random variable whose PDF is of the form, The (normalized) power of the same signal is given by P= A2. Find the PDF of ...An Erlang Random variable has a PDF of the form (a) Find the characteristic function, ϕX( ω) . (b) Find the Taylor series expansion of ϕX( ω) . (c) Find a general expression for the k th moment of X. For a Poisson random variable whose PMF is given by Find the following: (a) The probability- generating function, HX( z) , (b) The Taylor series expansion of HX( z) about the point z = 1 , (c) A general expression for the ...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.Post your question

0