SECTION 4.4 Summary

• A random variable is a variable taking numerical values determined by the outcome of a random phenomenon. The probability distribution of a random variable tells us what the possible values of are and how probabilities are assigned to those values.
• A random variable and its distribution can be discrete or continuous.
• A discrete random variable has possible values that can be given in an ordered list. The probability distribution assigns each of these values a probability between 0 and 1 such that the sum of all the probabilities is 1. The probability of any event is the sum of the probabilities of all the values that make up the event.
• A continuous random variable takes all values in some interval of numbers. A density curve describes the probability distribution of a continuous random variable. The probability of any event is the area under the curve and above the values that make up the event.
• Normal distributions are one type of continuous probability distribution.
• You can picture a probability distribution by drawing a probability histogram in the discrete case or by graphing the density curve in the continuous case.