questions: stats:

Exercise 9.1 a) Entropy of a random variable (2 Points) Let X be a discrete random variable with finite state space {0, 1, 2, 3} and distribution 3 P[X = k] = Poi(X)(k) for i = 1, 2,3 and P[X = 0] =1 - > Poi(X)(i) i=1 We will set A = }. Poi(X) here stands for a Poisson-distribution with parameter A, i.e. P[X = k] = k! Please calculate the entropy of random variable X. Exercise 9.1 b) Entropy of a random variable (2 Points) Consider the following two-stage experiment: We first throw a six-sided die. If the result is 6, we draw a ball from urn A. Otherwise, we draw from urn B. Urn A contains 2 black balls and 3 white balls. Urn B contains 3 red balls and 4 blue balls. Let X be the color of the ball drawn. Calculate the entropy of X