Topics: Probability - Distribution Function


Let be a random variable that handles a single Bernoulli trial as follows:

Let be the probability of success.

In such a case, we say that has a Bernoulli distribution and write .

Density Function


The density function of such an is given by:

Distribution Function


As for the distribution function of such an :

Expected Value


When it comes to the expected value of such an :



For the variance of such an :

Moment-Generating Function


Such an has its moment-generating function given by:

Characteristic Function


Finally, the characteristic function of is given by: