Gaussian sensor fusion:

Suppose we have two sensors with known (and different) variances Vx and Vy, but unknown (and the same) mean ?. Suppose we observe nx observations from the first sensor and ny observations from the second sensor. Call these Vx and Vy. Assume all distributions are Gaussian. What is the posterior p( mu | Dx , Dy ), assuming a non-informative prior for mu? Give an explicit expression for the posterior mean and variance.

(b) Suppose the y sensor is very unreliable. What will happen to the posterior mean estimate? Give a simplified approximate expression.