What does Binomial mean… why is it called Binomial Distribution?
The name for the binomial distribution comes from the fact the Binomial coefficient is part of the probability mass function. The “n choose x” part of the pmf is the binomial coefficient when for the xth term of the binomial expansion (z+y)^n Let X be the number of success in n trials. X has the binomial distribution with, for example here, n = 5 trials and success probability p = 0.72 In general, if X has the binomial distribution with n trials and a success probability of p then P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x) = nCx p^x (1-p)^(n-x) for values of x = 0, 1, 2, …, n P[X = x] = 0 for any other value of x. The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n – x failures. Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.
