Consider a geometric random variable, Z , whose PMF is PZ( k) = ( 1 – p) pk , k = 0,1,2, … . Find the entropy of this random variable as a function of p.
Answer to relevant QuestionsImagine that you are trapped in a circular room with three doors symmetrically placed around the perimeter. You are told by a mysterious voice that one door leads to the outside after a 2- h trip through a maze. However, the ...Find the mean of the random variables described by each of the following probability density functions: (a) (b) (c) (d) 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 . Let X be a random variable with E[X] = 1 and var(X) = 4. Find the following: (a) E [2X – 4]; (b) E[X2]; (c) E [(2X – 4) 2]. A uniform random variable has a PDF given by fX (x) = u(x) – u (x – 1). (a) Find the mean and variance of X. (b) Find the conditional mean and the conditional variance given that 1 / 2 < X < 3 / 4.
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