A random signal X can be observed only in the presence of independent addictive noise N. The observed quantity is Y = X + N.The joint probability density function of X and Y is
f(x,y) = K exp[-(x2 + y2 + 4xy)] all x and y
a. Find a general expression for the best estimate of X as function of the observation Y =y.
b. If the observed value of Y is y = 3, find the best estimate of X.