Binomial Distribution

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

• a histogram of the probabilities P( X = k )
• a table of their values from k_min to k_max
• the probability P( k_min < X < k_max)

Theory:

n balls are randomly drawn from a container containing a proportion p of red balls. The random variable X stands for the number of red balls drawn. The probability that k of the balls drawn are red, is given by P(X=k) = b(k;n;p).

The values for n and p are entered, where p must be between 0 and 1. Then a simple histogram gives a first overview of the values of P(X=k). The numerical values are output in a table of values.

Example:

  n = 60;    p = .75

     k           P(X=k)          P(0 ≤ X < k)
  ——    ——————   ——————
    40      0,03834033      0,09248427
    41      0,05610780      0,14859207
    42      0,07614630      0,22473838
    43      0,09562559      0,32036397
    44      0,11083875      0,43120273
    45      0,11822800      0,54943073
    46      0,11565783      0,66508856
    47      0,10335381      0,76844237
    48      0,08397497      0,85241733
    49      0,06169589      0,91411323
    50      0,04071929      0,95483252
  ——    ——————   ——————
  P(40 ≤ k < 50) =           0,90068858

See also:

Wikipedia: Binomial distribution