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1. [20 marks] We let (7% : n 2 1) be a sequence of independent exponential random variables, each having mean E[T,] = 1. We define for n 2 4, the random variable S, = 1 if T, = max (7m, T.-1, T.-2. .-3); otherwise, we define S. = 0. Also let S1 = S, = Sy = 0. (a) [10 marks] Determine the mean and variance of S, for n 2 4. (b) [10 marks] Determine the covariance Cov(S., So+1) for n 2 4