Statistics Chapter 5
- Review -

A random variable is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure.
A probability distribution is a description that gives the probability for each value of the random variable. It is often expressed in the format of a graph, table, or formula.

A discrete random variable has either a finite number of values or a countable number of values, where “countable” refers to the fact that there might be infinitely many values, but they can be associated with a counting process, so that the number of values is 0 or 1 or 2 or 3, etc.
A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale without gaps or interruptions.
Examples: 1.) Discrete: x = the number of eggs that a hen lays in a day. This is a discrete random variable because its only possible values are 0, or 1, or 2, and so on. No hen can lay 2.343115 eggs, which would have been possible if the data had come from a continuous scale. 2.) Continuous: x = the amount of milk a cow produces in one day. This is a continuous random variable because it can have any value over a continuous span. During a single day, a cow might yield an amount of milk that can be any value between 0 and 5 gallons. It would be possible to get 4.123456 gallons, because the cow is not restricted to the discrete amounts of 0,1,2,3,4, or 5 gallons.

Requirements for a Probability Distribution: 1.) Σ P(x) = 1 where x assumes all possible values. 2.) 0 ≤ P(x) ≤ 1 for every individual value of x.

Mean for a probability distribution:
Variance for a probability distribution:
Variance for a probability distribution (shortcut):
Standard deviation for a probability distribution:

Identifying Unusual Results with the Range Rule of Thumb