Let A and B be independent Gaussian random variables with A ∼ Normal (0, σ2 A) and B ∼ Normal (0, σ2 B). Define the stochastic process X(t) = At + B. One can interpret this relationship as the slope is a random variable A, and the y-intercept is a random variable B. (a) (16 points) Find the mean function mX(t) and the auto-covariance function CX,X (t1, t2) Is this process WSS? Why or why not? (b) (16 points) What is the linear least squares estimate of the intercept B based on the observation X(t0) = x0.
