What is a binomic division?
Binomic distribution with parameters (N, P) gives a discrete probability that x will have achievements from N trials, with the probability of success P, assuming that each study is independent and the result is either success or failure. The average number of successes from n trials is the average NP and the dispersion is NP (1-P). Binomial belongs to the family of related distributions related to events, including a negative binomia and Bernouilli's distribution. Because the probability of binomic distribution is calculated using a factorial function that increases greatly with increasing the number of experiments, binomic distribution of normal or Poisson distribution is usually used. The number of trials is n = 2 and the probability of throwing the head is p = ½. The results can be summarized in the binomial distribution table: The probability of head deficiency, P (x = 0) is 25%, the probability of one head, p (x = 1) is 50%and the probability of two heads P (x = 2) is 25%. The expected number of handball heads is np = 2*1/2 = 1. The dispersion is NP (1-P) = ½.
other distributions describe the likelihood of events and belong to the same family as binomial. Bernouilli distribution provides the likelihood of success of a single event and is equivalent to binomic with n = 1. Negative binomic distribution gives the probability of having a failure X where as a normal binomial gives probability of success X.
Often the function of the cumulative density of binomic distribution is used, which gives the probability that in n trials it will have x or less success. The calculation of this probability is simple for small n, but becomes tiring as it increases due to a binomic coefficient. The binomic coefficient is read "N Choose X" and refers to a OTUPLEDEER combination that X results can be selected from n options. It is calculated using a factorial function. Since the number of trials (N) is greater than 70, n factorial becomes huge and can no longer be calculated on a standard calculator.
approximation of binomic distribution, when N is enlarged, can be discreet or continuous. If n is very large and P is very small, then the binomic division becomes discreetly poisson distribution. If n is large enough without any restriction on P, binomic normal distribution of approximation can be used. The binomic medium and standard deviations become the parameters of normal distribution and correction for continuity is used to calculate the cumulative density function.