Question

Probability

A random signal X can be observed only in the presence of independent additive noise N.The observed quantity is Y = X+N. The joint probability density function of X and Y is

f(x, y)=K \exp \left[-\left(x^{2}+y^{2}+4 x y\right)\right] \quad \text { all } x \text { and } y

Find a general expression for the best estimate of X as a function of the observation Y=y.

. If the observed value of Y is y = 5, find the best estimate of X.


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