Theory

Theory 1

Expected value

The expected value of random variable is the weighted average of the values of , weighted by the probability of those values.

Discrete formula using PMF:

Continuous formula using PDF:

Notes:

• Expected value is sometimes called expectation, or even just mean, although the latter is best reserved for statistics.
• The Greek letter is also used in contexts where ‘mean’ is used.

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Let be a random variable, and write .

Variance

The variance measures the average squared deviation of from . It estimates how concentrated is around .

• Defining formula:

• Shorter formula:

Calculating variance

• Discrete formula using PMF:

• Continuous formula using PDF:

Standard deviation

The quantity is called the standard deviation of .