Minimum Mean-square-error Estimation

           Suppose is a random variable which is not observable and is another observable random variable which is statistically dependent on through the joint probability density function .We pose the following problem.

           Given a value of , what is the best guess for ?

           This problem is known as the estimation problem and has many practical applications.

One application is the signal estimation from noisy observations as illustrated in the Figure 1 below :

Figure 1