Binomial Definition and 668 Threads

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. S

    Question about Binomial expansion.

    I have my question and my problem in the attachment that followed.
  2. S

    Question regarding Binomial expansion.

    I have my question and my problem in the attachment that followed.
  3. R

    Understanding Binomial Theorem: How to Expand (a+b)^n

    Binomial Theorem... Hi I need to know about binomial theorem... eg. how to in general expand (a+b)^n I don't understand the combinations / permutations...? thanks Roger
  4. A

    Is -3 + 1/2x the Correct Inverse of 1/(2x+6)?

    the inverse of 1/(2x+6) x cannot=-3 is -3 + 1/2x ? Is this correct?
  5. N

    Solving Binomial Theorem Problems

    Hey. I am having difficultly with two math problems: 1. In the expansion of (mx+n)^5 the numerical coefficient of the second term is -48 and of the third term if 28.8 Find the values of m and n. 2. The first three terms in the expansion of (1+a)^n are 1-18+144. Determine the values of...
  6. D

    Expand & Sum Binomial Series: f(x)= x+x^2

    (a) Expand f(x)=\frac{x+x^2}{\left( 1-x\right) ^3} as a power series. (b) Use part (a) to find the sum of the series \sum _{n=0} ^{\infty} \frac{n^2}{2^n} \hline Here is what I've got: (a) f(x)=\frac{x+x^2}{\left( 1-x \right) ^3 } = \left( x + x^2 \right) \left[ 1...
  7. N

    Expected Value of X in Binomial Trials

    In a series of three binomial trials with p=.4, a random variable, X, is assigned to the outcomes to form a base 2 number, with 1 associated with success(S), and 0 associated with failure(F). For example, SFS->101=5. A) Find the expected value of X, E[X]. (Answer 2.80) B) Find the...
  8. B

    Understanding the Bias in Binomial Distribution for Probability Calculations

    binomial distribution Prob of rolling a 1 = 1/10, rolling a 2 = 2/10, 3 = 3/10, 4 = 4/10 Let X be the value thrown Calculate E(X) and Var(X) To do this can't use E(X) = np and can't use Var(X) = npq is this correct?
  9. T

    I need a proof for this binomial property.

    Hi, I've spent dozen of hours searching by my-self and dozen of hours searching on the Web. Now I need help. Who could provide a proof for this binomial property ? I need it for another proof. Thanks Tony Let: F_n=2^{2^n}+1 , n \geq 2 . Prove: F_n \text{ prime } \Longrightarrow F_n...
  10. S

    How Do You Solve Advanced Binomial Expansion Problems?

    Binomial Expansion problems!Please help me ASAP! 1)Using binomial expand (3X +4)^4.can you please kindly explain your process. 2)Use the first 4 terms in the binomial expansion of (3x+4)^4 in the DESCENDING order of x to determine the approx. of 1.004^12.Can you please give me the way how to...
  11. denian

    Minimum Occupants for Probability of Fishing > 0.7

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  12. H

    Binomial Distribution (Statistics)

    Hi guys, if you can help me with this problem it would be of great help 1) Pythag-Air-US Airlines has determined that 5% of its customers do not show up for their flights. If a passenger is bumped off a flight because of overbooking, the airline pays the customer $200. What is the expected...
  13. C

    Finding Coefficient of x^25 in (2x - (3/x^2))^58

    I get a number that is too big when I calculate the coefficient of x^25 in: (2x - (3/x^2))^58 This is how I found the coefficient: Note that (58) = A combination value... k (58) * (2x)^(58-k) * (-3/x^2)^k k (58) * (2)^(58 - k) * (x)^(58 - k) * (-3)^k * (1/x^2)^k k...
  14. Elkay

    Help with Series and Binomial Relativity Problems

    I need help with 2 series problems: http://fantasyland.250free.com/Series.jpg I was able to solve part a, but I don't understand part b or part c. http://fantasyland.250free.com/binomial_relativity.jpg I don't get this one at all. Any help would be appreicated.
  15. gimpy

    Proving the Max Binomial Coefficient for n and r

    Hi, I am having a little trouble with this proof: Let n be a positive integer. What is the largest binomial coefficient C(n,r) where r is a nonnegative integer less than or equal to n? Prove your answer is correct. So let r = \lfloor{\frac{n}{2}\rfloor} or r = \lceil{\frac{n}{2}\rceil}...
  16. B

    What distribution would you expect for these scenarios?

    What sort of distribution (eg binomial, normal..) would you expect each of the following to be? I am trying to get my head around all of these, so any help will be appreciated! 1)the number of goals scored during a football match 2)the height in inches of an individual 3)the number of...
  17. denian

    Binomial Expansion: Answer and Working for 1 + x/2 - x^2 to nth Power

    try this out.. expand ( 1 + x/2 - x to the power of 2 ) to the power of n in ascending powers of x until and including the term in x to the power of 3. the answers given by the book is 1 + nx/2 + n(n-9)/8 x to the power of 2 + n(n-1)(n-26)/48 x to the power of 3 + ... i just...
  18. Oxymoron

    Struggling with Binomial Series Expansion? Get Help Here!

    I have been doing some questions on Binomial Series expansion and have been stuck on this particular question for a long time and desperately need some guidance. Q) Expand (1/(sqrt(1-b^2(sin^2)x)))), where b = sin(1/2(theta)) as a binomial series. Here is what I have done so far... Let...
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