Question: 3. Let A be a random variable. Its rate function was defined in class as I(x) := sup sx - log M (s), where M(s)

3. Let A be a random variable. Its rate function was defined in class as I(x) := sup sx - log M (s), where M(s) := E(esx). Compute the rate function of each of the following random variables. (a) X is Gaussian with mean u and variance o2. (b) X is exponential with mean 1/1. (c) X is Poisson with mean 1. (d) X is one with probability p and zero with probability 1 - p

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