## (Solution Download) The probability density of a point x with respect to

The probability density of a point x with respect to a multivariate normal distribution having a mean ? and covariance matrix ? is given by the equation

Using the sample mean  and covariance matrix S as estimates of the mean ? and covariance matrix ?, respectively, show that the log(prob(x)) is equal to the Mahalanobis distance between a data point x and the sample mean  plus a constant that does not depend on x.

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