Say we have B and C that are two standard normal random variables with mean 0 and variance 1. Oh yeah, B and C are independent. Now say we have A = 2B + 3C. Say now that we found out A takes the value a = 2. I would like to calculate the MAP estimator of B for this scenario and I already know that the variance of A is 13 and its mean is 0. I also know that A and B are of course not independent. To calculate the MAP of B in this scenario, given A=2, it basically means to maximize the numerator of which consists of P(B) * P(A=a|B). But since we're dealing with a normal distribution, this is equivalent to minimizing the quadratic function of the exponential, since the other parts do not depend on B. I know that I have to take the derivative and set to zero, but I am not sure, if I have the parts of the quadratic function figured out correctly. If A was just B + C, then it would be easy: the essential parts of the exponential (those depending on B) would be 1/2*B^2 (for P(B)) +