AP Statistics - Chapter 6 Review

A random variable is a numerical outcome of a random phenomenon. It can be discrete (taking specific values) or continuous (taking any value within a range).

The mean (or expected value) of a random variable is the average of all possible values, weighted by their probabilities.

The standard deviation measures the dispersion or spread of a set of values around the mean. A higher standard deviation indicates more variability.

The mean of the sum of two independent random variables is the sum of their means: E(X + Y) = E(X) + E(Y).

The standard deviation of the sum of two independent random variables is the square root of the sum of their variances: SD(X + Y) = √(Var(X) + Var(Y)).

A discrete random variable is one that can take on a countable number of distinct values, such as the number of students in a class.

A continuous random variable can take on an infinite number of values within a given range, such as the height of students.

Variance is calculated as the average of the squared differences from the mean: Var(X) = E[(X - μ)²].

In a normal distribution, the mean indicates the center, while the standard deviation indicates the spread of the data around the mean.

The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the original distribution.