AP®︎ Statistics: Unit 2 Flashcards
Master key terms and definitions for Unit 2 of AP Statistics – Probability, Random Variables, and Probability Distributions to help you prep for quizzes and the AP exam.
Two-Way Table / Contingency Table
Table for two categorical variables; rows and columns are categories, and each interior cell is one category combination, with row totals, column totals, and a grand total
Table for two categorical variables; rows and columns are categories, and each interior cell is one category combination, with row totals, column totals, and a grand total
The count of individuals or outcomes in a category or event
A frequency divided by the total count; the proportion or percent in a category or event
Bar chart for two categorical variables with separate bars for categories of one variable within each category of the other; bars may show frequency or relative frequency
Bar chart with one equal-length bar for each group, divided into segments for the other variable; each bar represents 100% of that group
Display of a two-way table using rectangles; widths show group size, heights show conditional distribution within each group, and area shows cell frequency or joint relative frequency
For two categorical variables, the conditional distribution of one variable differs across categories of the other; equivalently, knowing one variable gives information about the other
Interior cell frequency divided by the grand total; proportion of all individuals in a particular combination of categories
Row total or column total divided by the grand total; describes one variable’s distribution ignoring the other
Cell frequency divided by the total for the conditioning row or column; describes a distribution within a specified category of the other variable
A repeatable process whose results are determined by chance
The result of one trial of a random process
A specified collection of outcomes
Using one chance process to imitate a real random process and estimate a probability from the relative frequency of an outcome or event
For many independent repetitions of a random process under the same conditions, the proportion of times E occurs approaches P(E)
For independent trials, as the number of trials increases, the relative frequency of an outcome or event approaches its probability
The set of all possible nonoverlapping outcomes of a random process, commonly denoted S; P(S) = 1
When outcomes in a finite sample space are equally likely, P(E) = number of outcomes in E divided by total number of outcomes in S
The event that E does not occur; all outcomes in the sample space not in E; written E′, Ē, or E^C
Two events that cannot both occur in the same trial; they have no outcomes in common, so P(A ∩ B) = 0
A ∩ B; the event of all outcomes that belong to both A and B, and its probability P(A ∩ B), the probability that both occur
Probability of A given that B has occurred; P(A|B) = P(A ∩ B) / P(B), provided P(B) > 0
P(A ∩ B) = P(A)P(B|A), or equivalently P(A ∩ B) = P(B)P(A|B)
Events where knowing whether one occurs does not change the probability of the other; equivalently, when defined, P(A|B)=P(A) or P(B|A)=P(B), and P(A ∩ B)=P(A)P(B)
A ∪ B; the event that A or B or both occur
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
A variable that assigns a numerical value to each outcome of a random process
A random variable with a finite or countably infinite set of possible values
For a discrete random variable, a list, table, graph, or function giving every possible value and its probability
A table or function giving F(x)=P(X≤x), the probability that a discrete random variable is less than or equal to x
Numerical characteristic of a probability distribution or population; a single fixed value
E(X) or μ_X; the probability-weighted average of possible values, μ_X = Σ x_i P(X = x_i)
SD(X) or σ_X; σ_X = √(Σ (x_i - μ_X)² P(X = x_i)), the typical distance of values from the mean
V(X), Var(X), or σ_X²; V(X) = Σ (x_i - μ_X)² P(X = x_i)
A discrete random variable that counts the number of successes in a fixed number n of independent trials with binary outcomes and the same success probability p
Notation that X has a binomial distribution with n trials and probability of success p on each trial
P(X = x) = (n choose x)p^x(1 − p)^(n − x), for x = 0, 1, ..., n; gives the probability of exactly x successes
A variable that can take any value in an interval; probabilities are assigned to intervals, not single points
A continuous probability distribution with a unimodal, bell-shaped, symmetric density curve, determined by mean μ and standard deviation σ.
The normal distribution with mean 0 and standard deviation 1; written Z ~ N(0,1)
For a normal distribution, about 68% of values lie within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3
For a normal random variable, the probability of an interval equals the area under the curve over that interval; total area is 1
A standardized value showing how many standard deviations a raw value is above or below the mean: z = (x - μ)/σ.
The pth percentile is a value with about p% of the distribution at or below it
Distribution of a statistic’s values for all possible samples of a fixed size from a given population using the same random sampling process
Distribution of a statistic generated by repeatedly randomly reallocating or reassigning observed response values to treatment groups and recalculating the statistic
For the mean x̄ of a random sample, the sampling distribution can be approximated by a normal distribution; the larger the sample size, the better the approximation
