For this problem, we use the following notation for random variables: . X ~ N(u, 02): X is a Gaussian random variable with mean u and variance o2 . X ~ Bern(p): X is a {0, 1}-valued Bernoulli random variable with expectation p. . E[X]: the expected value of random variable X(a) If X ~ N(1, 2), then what is E[X]? What is E[X2] - E[X]?? (b) If X1, X2, ..., Xn be independent random variables with Xi ~ Bern(p), i = 1, 2, ...,n, what is the distribution of Et-1 Xi? c Let assume the sequence {0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1} is independently drawn from Bern(p) (multi- ple flips of a biased coin with probability of being head as p which is unknown). What is the maximum likelihood estimator (MLE) of p? Please show the detailed steps (and mathematical derivations you employ to get the MLE estimator)