Problem 1 Consider the stochastic process X(t) = e t, fort > 0, where Y is a random variable with a uniform distribution on the interval (0, 1). 1. (10 points) Calculate the first-order density function of the process {X(t) , t > 0} 2. (5 points) Compute E[X (t)], for t > 0. 3. (10 points) Compute the auto-covariance function Cx(t, t+s) for s, t > O. We still consider the same process X defined above but we no longer assume that Y is uniformly distributed in (0, 1). We only assume that Y has a density function fy(y) for y > 0. 4. (5 points) Calculate the density of the process {X(t), t > 0}, f(t, x), in terms of fy(y). 5. (10 points) Calculate E[X (t)] and Rx(t1, t2) when Y has an exponential distribution with parameter 1