Determining Probability Distributions

Abstract

There are many situations in which only one of two possible outcomes may be observed. A coin may fall heads or tails; an organism may be infected by a virus or not infected by it; a gene may be dominant or recessive. If we observe N events, there is a probability p(n) that n of them will turn out one way and N — n will turn out the other way. There are also probabilities that the number of outcomes of one kind will not be n, but some other number. Taken together, all probabilities constitute a distribution. The distribution of p(n) in which events can occur only one of two ways is the binomial distribution. This chapter introduces distributions using the binomial case (there are others) first for the situation that the probability of observing an event is the same as the probability of observing its opposite, as in the case of coin tossing. The chapter continues by describing cases in which the probabilities are different and concludes with applications in the biomedical field.