please show step by step solution

Question 3 LMMSE Suppose X is a temperature to be estimated and Y , Y2 are the measurements. In particular, Y; = X+Z Y2 = X +Z1 + Z2 a) Assume 21, 22 are independent noise, with zero means and variances 0,?,022. Derive the LMMSE estimator of X, given Y1, Y2. b) Suppose E[X] = 10, 0,2 = 1,022 = 10. Find the LMMSE estimator