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Unit 2 · Probability, Random Variables & Distributions Flashcards Cheat Sheet Essentials Visual Review MC Practice FRQ Practice

AP Statistics Unit 2 Essentials

The must-know terms and core concepts for Unit 2: Probability, Random Variables & Distributions. Every vocabulary word and idea you need to master.

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Key Concept 1
Probability is the long-run behavior of chance, governed by a few rules
Probability is the long-run relative frequency of an outcome (the Law of Large Numbers), and every problem reduces to a small set of rules. The addition rule handles 'or' (subtracting the overlap unless events are mutually exclusive); conditional probability, P(A | B) = P(A and B)/P(B), restricts the sample space to outcomes where B occurs; and events are independent when P(A | B) = P(A). Two-way tables and simulation are the concrete settings where these ideas first appear.
Probability Rules Conditional Probability Independence
Key Concept 2
Random variables turn chance outcomes into numbers with a distribution
A random variable assigns a number to each outcome, and its probability distribution lists those values with their probabilities (which sum to 1). Like a data set, a random variable has a center and a spread: the expected value E(X) = Σ x·P(x) and the standard deviation. When you combine random variables, means always add, and for independent variables variances add — a rule that returns constantly in later units.
Random Variables Expected Value Combining Variables
Key Concept 3
Two models — binomial and normal — plus sampling distributions power the rest of the course
The binomial distribution models a fixed number of independent success/failure trials (check BINS), with mean np and standard deviation √(np(1 − p)). The normal distribution — the bell curve — is described by z-scores and the 68–95–99.7 empirical rule. Finally, sampling distributions and the Central Limit Theorem explain why sample statistics behave predictably, which is exactly what makes the confidence intervals and tests of Units 3–5 possible.
Binomial Normal Sampling Distributions
Two-way table
A table showing counts for two categorical variables at once, with row and column totals.
Two Categorical Variables
Marginal relative frequency
A row or column total divided by the grand total.
Two Categorical Variables
Joint relative frequency
A single cell count divided by the grand total.
Two Categorical Variables
Conditional relative frequency
A cell divided by its row or column total; the distribution of one variable given the other.
Two Categorical Variables
Association
Present when the conditional distributions of one variable differ across categories of the other.
Two Categorical Variables
Probability
The long-run relative frequency with which an outcome occurs.
Probability
Law of Large Numbers
As trials increase, the observed proportion approaches the true probability.
Probability
Sample space
The set of all possible outcomes of a chance process.
Probability
Simulation
Imitating a chance process many times to estimate a probability.
Probability
Mutually exclusive (disjoint)
Events that cannot occur at the same time; P(A and B) = 0.
Probability Rules
General addition rule
P(A or B) = P(A) + P(B) − P(A and B).
Probability Rules
Conditional probability
P(A | B) = P(A and B) / P(B) — the probability of A given B.
Probability Rules
Independent events
Events for which P(A | B) = P(A); equivalently P(A and B) = P(A)·P(B).
Probability Rules
Multiplication rule
P(A and B) = P(A)·P(B | A), which becomes P(A)·P(B) when A and B are independent.
Probability Rules
Random variable
A variable that assigns a numerical value to each outcome of a chance process.
Random Variables
Probability distribution
A list of a random variable's values and their probabilities, which sum to 1.
Random Variables
Expected value (mean)
The long-run average of a random variable, E(X) = Σ x·P(x).
Random Variables
Standard deviation of a random variable
A measure of how much the variable's outcomes typically vary from the mean.
Random Variables
Binomial distribution
The distribution of the number of successes in n independent trials with the same probability p.
Distributions
BINS conditions
Binary, Independent, fixed Number, Same probability — the requirements for a binomial setting.
Distributions
Normal distribution
A symmetric, bell-shaped distribution described by its mean and standard deviation.
Distributions
z-score
(x − mean) / standard deviation; the number of standard deviations from the mean.
Distributions
Empirical rule
In a normal distribution, about 68%, 95%, and 99.7% of values fall within 1, 2, and 3 SDs of the mean.
Distributions
Central Limit Theorem
For large samples, the sampling distribution of the sample mean is approximately normal.
Distributions