Law of Bernoulli

See also: Theorem of Bernoulli

In Mathematical, the distribution of Bernoulli or law of Bernoulli , name of the Swiss mathematician Jacques Bernoulli, is a discrete distribution of Probabilité, which takes value 1 with the probability p and 0 with the probability $q = 1 - p$ .

$F (X) = \ left \ {\ begin {matrix} p & \ mbox {if} x=1, \ \ Q & \ mbox {if} x=0, \ \ 0 & \ mbox {if not.}\end{matrix}\right.$

The mathematical Espérance of a Random variable of Bernoulli is worth p and the Variance is worth $pq = p (1-p)$ .

The Kurtosis tends towards the infinite one for high and low values of p , but for $p=1/2$ the distribution of Bernoulli has a kurtosis low than any other distribution, i.e. 1.

The distribution of Bernoulli applies at the time of a test of Bernoulli whose success is 1 and failure 0.

Dependant distributions

If $X_1, \ dowries, X_n$ are random variables of Bernoulli with parameter $p$ , independent identically distributed, then $Y = \ sum_ {k=1} ^n X_k \ sim \ mathrm {Binomial} (N, p)$
(Binomial distribution).

Random links: