# Question: Suppose we flip a balanced coin five times and let

Suppose we flip a balanced coin five times and let the random variable represent the number of times heads occurs.

(a) Sketch the CDF of X fx (x).

(b) Write fx (x), analytically in terms of unit step functions.

(a) Sketch the CDF of X fx (x).

(b) Write fx (x), analytically in terms of unit step functions.

## Relevant Questions

Repeat Exercise 3.39 if is a Rayleigh random variable with PDF, (a) Find the conditional PDF, fv|{v > 1}(v) . (b) Find the conditional PDF, fv|{1/2 < v < 3/2}(v). (c) Find the conditional CDF,fv|{1/2 < v < 3/2}(v) fv (v) ...Suppose we are given samples of the CDF of a random variable. That is, we are given Fn = Fx (xn) at several points, xn Ɛ { x1, x2, x3,….xk. After examining a plot of the samples of the CDF, we determine that it appears ...Suppose X is a binomial random variable with parameters n and p . That is, the PMF of X is given by Find the PMF of a new random variable generated through the transformation, Y= n–X. For 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. 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 ...Post your question