Topics: Probability - Bernoulli Distribution


Let be a random variable that handles the repetition of Bernoulli trial (: the number of successful trials). Let be the number of independent Bernoulli trials and be the probability of success.

In such a case, we say that has a binomial distribution and write it as .

Density Function


The density function of an such that distribution is given by:

Expected Value


The expected value of such an is:



The variance of such an is:

Moment-Generating Function


Finally, the moment-generating function of such an is: