Let (, ) be k independent, normally distributed random variables with means and variances .

It is easier to write out the likelihood function of a set of independent identically distributed categorical variables.

Interactive Flash simulation on the correlation of two normally distributed variables.

Assuming that the win/loss outcomes of each bet are independent and identically distributed random variables, the stopping time has finite expected value.

Consider n jointly distributed random variables with a joint probability density function .

The terms in the similar segment are eliminated and the difference becomes a scaled difference between two uniformly distributed random variables.

It is important to know that the interval parameters generate different results than uniformly distributed random variables.

Let X be a set of independent Rademacher distributed random variables.

However, a pair of jointly normally distributed variables need not be independent (would only be so if uncorrelated, ).

The buyer's types, or valuations of the object, are independent identically distributed random variables.