1. (30 points) Let N be a random variable representing the outcome of a fair dice...

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1. (30 points) Let N be a random variable representing the outcome of a fair dice roll. Let X; be a binary random variable (0 and 1) representing the outcome of the i-th fair coin flip. We define a random variable Z E X, and denote its pmf by p(Z). (a) (b) Calculate the mean of Z. Calculate the variance of Z. (c) Calculate E[log2(1/p(Z)) = -E: p(2) log2 p(2), which is called the entropy. 1. (30 points) Let N be a random variable representing the outcome of a fair dice roll. Let X; be a binary random variable (0 and 1) representing the outcome of the i-th fair coin flip. We define a random variable Z E X, and denote its pmf by p(Z). (a) (b) Calculate the mean of Z. Calculate the variance of Z. (c) Calculate E[log2(1/p(Z)) = -E: p(2) log2 p(2), which is called the entropy.