Discrete Distribution

For all the definition below:

• is the population size.
• is the sample size.

Parameters

Mean

Average of the all values in the entire population. Usually unknown. Denoted by .

Variance

Measure of the spread of the observed values. Denoted by .

Standard Deviation

Square root of the variance. Denoted by .

Skewness

Sample Parameters

Sample mean

Average of the observed values. Denoted by .

Sample variance

Denoted by .

Here sample mean is used instead of , which underestimates the variance. is used instead of to correct this bias, which is called Bessel’s correction. This correction makes it an unbiased estimator.

Sample covariance

Sample skewness