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
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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