Binomial Distribution

{
  "id": "MLC-T-ENV-003115",
  "term": "Binomial Distribution",
  "field": "Environment",
  "definition": "1. The statistical distribution of the probabilities of observing 0,1,2,- - - ,n events in a sample of n independent trials each with the same individual probability that the event occurs.\n\n2. The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are appropriately labeled \"success\" and \"failure.\" The binomial distribution is used to obtain the probability of observing x successes in N trials, with the probability of success on a single trial denoted by p. The binomial distribution assumes that p is fixed for all trials. The formula for the binomial probability mass function is [See PDF page 126 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf].\n\n3. A family of discreet probability density functions, which models systems that meet the following requirements: 1) the number of trials (n) is fixed; 2) there are only two outcomes for each trial, success or failure; 3) the outcome of each trial is independent; and 4) all trials have the same probability (p) of success. Binomial distributions show the likelihood of the number of successful trials versus the total number of trials.\n\n4. The probability distribution associated with two mutually exclusive outcomes; used to model cumulative incidence rates and prevalence rates. The Bernoulli distribution is a special case of binomial distribution. (CancerWEB 2005)\n\n5. Statistical distribution of the probabilities of observing 0,1,2,- - - ,n events in a sample of n independent trials each with the same individual probability that the event occurs.\n\n6. The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are appropriately labeled \"success\" and \"failure.\" The binomial distribution is used to obtain the probability of observing x successes in N trials, with the probability of success on a single trial denoted by p. The binomial distribution assumes that p is fixed for all trials.",
  "subject": "Science and research",
  "references": [
    "Benchmark Dose Software (BMDS) Glossary of Terms",
    "Thesaurus of Terms Used in Microbial Risk Assessment",
    "National Cancer Institute Thesaurus",
    "Adapted from Thesaurus of Terms Used in Microbial Risk Assessment"
  ],
  "url": "https://mlchart.com/terminology/environment/binomial-distribution/"
}