Continental Congress. Franklin returned to Philadelphia in 1775. There he served as a delegate to the Continental Congress, where he was instrumental in drafting the Declaration of Independence and the Articles of Confederation to form a new union.
In its simplest form (when r is an integer), the negative binomial distribution models the number of failures x before a specified number of successes is reached in a series of independent, identical trials. Its parameters are the probability of success in a single trial, p, and the number of successes, r. A special case of the negative binomial distribution, when r = 1, is the geometric distribution, which models the number of failures before the first success. More generally, r can take on non-integer values.
The binomial distribution is therefore given by P_p(n|N) = (N; n)p^nq^(N-n) (1) = (N!)/(n!(N-n)!)p^n(1-p)^(N-n), (2) where (N; n) is a binomial coefficient. The above plot shows the distribution of n successes out of N=20 trials with p=q=1/2. The...