What is Binomial: Definition and 667 Discussions

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution remains a good approximation, and is widely used.

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  1. T

    The normal approximation to the binomial

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  2. L

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    MHB What is the Least Value of K for Advancement in a Binomial Distribution Game?

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  9. C

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  11. J

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  12. P

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  13. S

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  14. N

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  15. B

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  17. A

    Probability of 5 Heads in Binomial Distribution

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  18. Z

    Binomial identities,combinatorial, equivalence

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  19. A

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  20. L

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  21. F

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  30. 8

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  37. M

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  39. H

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  40. Z

    Binomial identities,combinatorial, equivalence

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  41. I

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  50. S

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