Difference between revisions of "Binomial distribution"

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Consider an event—such as a coin coming down heads—that can be true or false in each trial—or each toss—with probability ''p'' -- it has a Bernoulli distribution. A binomial distribution describes the number of times an event is true -- e.g., the coin is heads -- in ''n'' independent trials—or tosses—where the event occurs with probability p on each trial.
 
Consider an event—such as a coin coming down heads—that can be true or false in each trial—or each toss—with probability ''p'' -- it has a Bernoulli distribution. A binomial distribution describes the number of times an event is true -- e.g., the coin is heads -- in ''n'' independent trials—or tosses—where the event occurs with probability p on each trial.
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The Binomial distribution is a non-negative discrete distribution where the probability of outcome ''k'' is given by
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:<math>P_{n,p}(k) = \left(\begin{array}{c}n\\k\end{array}\right) p^k (1-p)^{n-k}</math>
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The distribution has a [[Mean]] of <code>n*p</code> and a [[Variance]] of <code>n*p*(1-p)</code>.
  
 
= Library =
 
= Library =

Revision as of 20:09, 23 January 2012


BinomialDistribution.png

Binomial( n,p )

Consider an event—such as a coin coming down heads—that can be true or false in each trial—or each toss—with probability p -- it has a Bernoulli distribution. A binomial distribution describes the number of times an event is true -- e.g., the coin is heads -- in n independent trials—or tosses—where the event occurs with probability p on each trial.

The Binomial distribution is a non-negative discrete distribution where the probability of outcome k is given by

[math]\displaystyle{ P_{n,p}(k) = \left(\begin{array}{c}n\\k\end{array}\right) p^k (1-p)^{n-k} }[/math]

The distribution has a Mean of n*p and a Variance of n*p*(1-p).

Library

Distributions

See Also

  • CumBinomial -- the analytica cumulative probability function for Binomial
  • Prob_Binomial -- the analytic probability function for Binomial
  • Multinomial -- A generalization of Binomial in which more than two outcomes are possible.
Comments


Marksmith

102 months ago
Score 0
It would still be useful to have a built-in function, say Binomial(n,p,k1,k2) that samples from the conditional Binomial distribution X|k1<=X<=k2. UDFs for the conditional Poisson are easier to write and operate quicker than for the conditional Binomial.
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Lchrisman

79 months ago
Score 0
Mark -- Try: Truncate( Binomial(n, p), k1, k2 )
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