AP Statistics Unit 4 Part 1

Random variable

A variable whose value is a numerical outcome of a random process.

Discrete random variable

A random variable that takes a countable set of possible values, with gaps between values.

Probability distribution

A description of the possible values of a random variable and the probability of each value.

Expected value

The mean of a random variable; its long-run average value over many repetitions.

Continuous random variable

A random variable that can take any value in an interval of numbers.

Density curve

A model for a continuous distribution; the area under it is 1, and area over an interval gives its probability.

Normal distribution

A symmetric, bell-shaped continuous distribution described by its mean and standard deviation.

Empirical rule

For an approximately normal distribution, about 68%, 95%, and 99.7% of values fall within 1, 2, and 3 standard deviations of the mean.

Standard normal distribution

A normal distribution with mean 0 and standard deviation 1.

Variance

The square of the standard deviation; a measure of spread in squared units.

Standard deviation

A measure of the typical distance of a random variable's values from its mean.

Independent random variables

Random variables for which knowing one value does not change the probability distribution of the other.

Linear transformation

A change to a random variable of the form a + bX, where a and b are constants.