To understand probability distributions, it is important to understand variables. random variables, and some notation. A variable is a symbol ( A , B , x , y , etc.) that can take on any of a specified set of values. When the value of a variable is the outcome of a statistical experiment, that variable is a random variable . Generally, statisticians use a capital letter to represent a random variable and a lower-case letter, to represent one of its values. For example, X represents the random variable X. P(X) represents the probability of X. P(X = x) refers to the probability that the random variable X is equal to a particular value, denoted by x. As an example, P(X = 1) refers to the probability that the random variable X is equal to 1. Probability Distributions An example will make clear the relationship between random variables and probability distributions. Suppose you flip a coin two times. This simple statistical experiment can have
Statistical analysis often uses probability distributions