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. L

    I Problems that could occur in estimating n from a Binomial distribution

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  2. J

    A Newton's Generalized Binomial Theorem

    I'm trying to expand the following using Newton's Generalized Binomial Theorem. $$[f_1(x)+f_2(x)]^\delta = (f_1(x))^\delta + \delta (f_1(x))^{\delta-1}f_2(x) + \frac{\delta(\delta-1)}{2!}(f_1(x))^{\delta-2}(f_2(x))^2 + ...$$ where $$0<\delta<<1$$ But the condition for this formula is that...
  3. Pushoam

    Why Does Calculating Binomial Probabilities Differ from Simple Outcome Ratios?

    Homework Statement I am not getting the above. Let me calculate the probability of getting 2 successes from 5 Bernoulli trials. There are total 10 possible outcomes as each trial has two possible outcomes. The probability of getting one success is P(S1) = No. of successes / no. of total...
  4. bdolle

    What is the Correct Way to Write a Binomial Expansion for (1+(1/x))^(-3/2)?

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  5. T

    Calculating Binomial Probability for Car Color Preferences

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  6. D

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  7. lfdahl

    MHB Binomial coefficient challenge

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  8. O

    Why isn't this a binomial distribution?

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  9. K

    I About binomial statistics

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  10. lfdahl

    MHB Prove an identity with binomial coefficients

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  11. I

    I Need closed form for a Binomial series

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  12. Schaus

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  13. Schaus

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  14. C

    Help with basic binomial coefficient

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  15. R

    B Issue with Binomial Expansion Formula

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  16. RJLiberator

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    Homework Statement A good hitter in baseball has a batting average of .300 which means that the hitter will be successful three times out of 10 tries on average. Assume that the batter has four times at bat per game.a) What is the probability that he will get two hits or less in a three game...
  17. M

    MHB Binomial Expansion - Fractional Powers

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  18. Alettix

    B Binomial Expansion with Negative/Rational Powers

    Hello! When studying binominal expansion: ## (a+b)^n = \sum_{k=0}^{n}{{n \choose k}a^{n-k}b^k} ## in high school, we proved this formula with combinatorics considering that "you can choose either a or b each time you multiply with a binom". Probably, this is not a real mathematical proof at...
  19. J

    MHB Calculate Upper Bound for $\displaystyle a_{n}$ in Binomial Limit Evaluation

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  20. A

    I Summation for extended binomial coefficients

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  21. M

    MHB Comparing Binomial & Binary Heaps: What's the Difference?

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  22. L

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  23. P

    MHB Binomial Probability - Again.

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  24. MOHD ZAKI

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  25. T

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  27. P

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  28. A

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  30. amind

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  31. K

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  32. M

    MHB Solve Sum of {30 \choose i} with Binomial Theorem

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  33. C

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  34. 3301

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  35. M

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  36. Q

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  38. P

    MHB Prob of red ball in buckets. Binomial?

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  39. Orange-Juice

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  40. A

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  41. alexmahone

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  42. Y

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  43. SSGD

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  44. Destroxia

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  45. Odious Suspect

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  46. JonnyMaddox

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  47. G

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  48. T

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  49. sunrah

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  50. T

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