an error with zero mean and variance Similarly, the second pollster declares their estimate to be with an error with zero mean and variance Note that except for the mean and variance of the error, the error distribution is unspecified. How should the two polls be combined to obtain the voting prediction for the given candidate? As with previous example, we have Here, both the . Thus, we can obtain the LMMSE estimate as the linear combination of and as where the weights are given by Here, since the denominator term is constant, the poll with lower error is given higher weight in order to predict the election outcome. Lastly, the variance of is given by which makes smaller than Thus, the LMMSE is given by In general, if we have pollsters, then where the weight for i-th pollster is given by and the LMMSE is given by Example 4 Suppose that a musician is playing an instrument and that the sound is received by two microphones, each of them located at two different places. Let the attenuation of sound due to distance at each microphone be and , which are assumed to be known constants. Similarly, let the noise at each microphone be and , each with zero mean and variances and respectively. Let denote the sound produced by the musician, which is a random variable with zero mean and variance How should the recorded music from these two microphones be combined, after being synced with each other? We can model the sound received by each microphone as Here both the . Thus, we can combine the two sounds as where the i-th weight is given as See also Bayesian estimator Mean squared error Least squares Minimum-variance unbiased estimator (MVUE) Orthogonality principle Wiener filter Kalman filter Linear prediction Zero-forcing equalizer Notes Further reading Statistical deviation and dispersion Point estimation performance Signal estimation