A Short Overview
1. The binomial distribution (‘coin-flipping’ model): X is the number of successes in n independent trials (success or failure), p is the fixed probability of success. This is the ‘yes/no sampling with replacement from a finite population’ function. The binomial model also gives good approximations when sampling without replacement, as long as the sample size is very small compared to the population size.
So ‘true (1) and false (0)’ are answers to the question “Cumulative?”
2. The Poisson distribution (‘number of occurrences per unit of measure’ model):
Assumes the units (minutes, hours, miles, acres, etc.) are independent. Assumes that the mean number of occurrences per unit is known.
3. The Hypergeometric distribution (‘number of successes in sample’ model):
x is the number of ‘successes’ (or just occurrences of some characteristic) in a sample of size n randomly selected from a ‘population’ size N containing M successes (or occurrences of the characteristic). This is the ‘yes/no sampling without replacement from a finite population’ function. If the sample size is small compared to the population size, the binomial distribution gives a good approximation to the hypergeometric.
4. The Insert Tab can be used to make a histogram of these probability models if a probability table is computed first. For example if X is binomial with n = 10 and p = .75,
the probability distribution and histogram are as given on the next page.