Mean and Covariance Matrix of a Random Variable
If is a vector random variable, the mean of is , where denotes the expectation operator with respect to the distribution that follows. The covariance matrix of is defined as
Note that the covariance matrix is always a positive semi-definite matrix.
Assume that the distribution is discrete, with the probability that the random variable takes a certain value , . Then the expected value of is
and the covariance matrix is
Example: if takes the two values , with
with the probability of (resp. ) being (resp. ), then the mean of is
and its covariance matrix is
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