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. ArcanaNoir

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  2. S

    Description of binomial expansion

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  3. M

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  4. K

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  5. J

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  6. S

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  7. S

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  8. S

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  9. R

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  10. K

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  11. P

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  12. P

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  13. E

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  14. W

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  15. P

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  16. L

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  17. J

    Newton's Binomial Theorem to Estimate, Find Error

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  18. E

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  19. Rasalhague

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  20. Rasalhague

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  21. Q

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  22. F

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  23. B

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  24. noowutah

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  25. T

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  26. P

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  28. J

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  29. S

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  30. B

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  31. I

    Power and binomial distribution

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  32. A

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  33. X

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  34. O

    Conditional Probability and/or Binomial Distribution(s)

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  35. coolul007

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  37. B

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  38. K

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  39. G

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  40. M

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  41. M

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  42. K

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  43. G

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  44. mnb96

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    Hello, I considered a Binomial distribution B(n,p), and a discrete random variable X=\frac{1}{n}B(n,p). I tried to compute the characteristic function of X and got the following: \phi_X(\theta)=E[e^{i\frac{\theta}{n}X}]=(1-p+pe^{i\theta/n})^n I tried to compute the limit for n\to +\infty...
  45. S

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  46. Z

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  47. A

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  48. R

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  49. Q

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  50. V

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