Stochastics

Binomial Distribution

For a b(k;n;p) distributed random variable X with fixed n and p you can calculate

Theory:

n balls are drawn with replacement out of a container with a portion p of red balls. The random variable X stands for the amount of red balls drawn. The probability of k of the balls drawn being red, is characterized by P(X=k) = b(k;n;p).

The values for n and p are entered, where p as probability has to lie between 0 and 1. After this, a simple histogram gives a first survey over the values of P(X=k). The numeric values are issued in a table of values.

Example:

n = 200            p = .75

    k         P(X=k)       P(0<=X<=k) 
  ------    ----------     ----------
  140       0,01708367     0,06247223
  141       0,02180894     0,08428117
  142       0,02718438     0,11146556
  143       0,03307750     0,14454306
  144       0,03927954     0,18382260
  145       0,04551008     0,22933268
  146       0,05143263     0,28076531
  147       0,05668085     0,33744616
  148       0,06089362     0,39833978
  149       0,06375439     0,46209418
  150       0,06502948     0,52712366
  151       0,06459882     0,59172248
  152       0,06247386     0,65419634
  153       0,05879893     0,71299527
  154       0,05383538     0,76683066
  155       0,04793086     0,81476151
  156       0,04147863     0,85624014
  157       0,03487375     0,89111389
  158       0,02847287     0,91958676
  159       0,02256341     0,94215017
  160       0,01734562     0,95949579
  ------    ----------     ----------
  P(140<=k<=160) =         0,91410723

See also:

Wikipedia: Binomial distribution
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