# Test of Bernoulli

In Probability, a test of Bernoulli of parameter p (real ranging between 0 and 1) is a random experiment (i.e. subjected randomly) comprising two exits:

• success
• the failure
Reality p represents the probability of a success. Reality Q = 1 - p represents the probability of a failure.

The definition of “success” and “the failure” is conventional and is function of the conditions of the experiment.

; Example 1

the to launch of a balanced part is an experiment of Bernoulli of parameter 0,5. If “success” is obtaining pile, “the failure” will be obtaining face.

; Example 2

One randomly draws a ball in a ballot box containing 7 white balls and 3 black balls. One regards as a success makes it draw a black ball. This experiment is an experiment of Bernoulli of parameter 0,3 because the probability of drawing a black ball is of 3/10.

On the universe {success, failure}, one can define a random variable X taking value 1 in the event of success and 0 in the event of failure. This random variable follows a law of Bernoulli. It has for hope p and for variance pq .

A succession of N independent tests of Bernoulli allows the construction of a random variable cash the number of successes. This random variable has as a law of probability the Binomial distribution of parameters ( N , p ).

To schematize the succession of several independent experiments of Bernoulli, one can build a Arbre of probability comprising 2 N final branches. This tree is called a diagram of Bernoulli .

## See too

• Probability (elementary mathematics)
• Bernoulli
• Distribution of Bernoulli

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