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Discrete random variance

The variance is, in short, a measure of how much the values of a random variable differ from the mean. It’s the square of the standard deviation.

We write the variance of a list of values as .

Suppose we have a list of possible discrete values and their probabilities.
The value at position is and the associated probability is .

The variance of the list is calculated by:

We can substitute the formula for expectation into this - - to get: