Let X and Y are two independent random variables. Suppose X - Normal(2,6) and Y-EXP(0.5). Someone who can observe X tries to estimate the sum Z = X + Y based on their observation of X. (a) If the observer uses the MMSE method for estimation, what would be the mean square error they would incur? Your answer here correct to four decimal places. (b) If the observer uses the MAP rule for estimation, what would be the mean square error they would incur? Your answer here correct to four decimal places. Let X and Y are two independent random variables. Suppose X - Normal(2,6) and Y-EXP(0.5). Someone who can observe X tries to estimate the sum Z = X + Y based on their observation of X. (a) If the observer uses the MMSE method for estimation, what would be the mean square error they would incur? Your answer here correct to four decimal places. (b) If the observer uses the MAP rule for estimation, what would be the mean square error they would incur? Your answer here correct to four decimal places