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. M

    Binomial Coefficients Identity

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  2. M

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  4. Z

    Binomial coefficient summation proof

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  5. E

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  6. P

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  7. N

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  8. T

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  9. G

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  11. R

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  12. M

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  13. M

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  14. M

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  15. L

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  16. P

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  17. S

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  18. D

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  19. Q

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  20. O

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  21. A

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  22. M

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  23. L

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  30. T

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  31. J

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  46. A

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  50. T

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