Probability and Statistics for Computer Scientists, 2nd Edition

Chapter 12

Appendix

12.1 Inventory of distributions

12.1.1 Discrete families

Bernoulli(p)

Generic description:	0 or 1, success or failure, result of one Bernoulli trial
Range of values:	x = 0, 1
Parameter:	p ∈ (0, 1), probability of success
Probability mass function:	P(x) = px(1 − p)1−x
Expectation:	μ = p
Variance:	σ2 = p(1 − p)
Relations:	Special case of Binomial(n, p) when n = 1
A sum of n independent Bernoulli(p) variables is Binomial(n, p)

Binomial(n, p)

Generic description:	Number of successes in n independent Bernoulli trials
Range of values:	x = 0, 1, 2,..., n
Parameters:	n = 1, 2, 3,..., number of Bernoulli trials
p ∈ (0, 1), probability of success
Probability mass function:	$p(x)=\left(\begin{array}{c}n\\ x\end{array}\right)p^{}$