## 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.