Binomial Distribution
For a b(k;n;p) distributed random variable X with fixed n and p you can calculate
- a histogram of the probabilities P( X = k )
- a table of their values from kmin to kmax
- the probability P( kmin < X < kmax)
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
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
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
