Well detailed answers and explanation for the following questions would be appreciated:

Exercise 2: Mutual Information and Entropy Consider two discrete random variables X and Y. We are told that both variables have the same pmf 13(59)- and support .it' = )2. We also know that H {Y} is strictly greater than zero. If we dene the parameter A = 1 H(Y|X} (H(X})-1, a) Show that A = I{X;Y}IH(X} and that U E A <_i marks b discuss the relationship between x and depending on a paying special attention to extreme values of parameter. c if you wish guess knowing y vice versa what is best value exercise mutual information sixsided fair dioe cube rolled. obtain random variable variables z i.e. hx where: x: number dots front face side facing y: top z: bottom consider game two teams. i for binary vari ables x1 that model outcome win or lose teams respectively team has probability winning game. it possible x2 bit do not simply answer mathematically give also an intuitive justication in terms variables. markov chain> Y > Z. Taking into account the mutual information between pairs of these variables, show that H (X |Zj 35 H (X |Y} and that H(Z|X} 33 H(Z|Y}. [5 marks]