AP Statistics Flashcards: Introduction to Random Variables and Probability Distributions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
A table lists the possible number of goals scored in a soccer game and the probability of each. What is this table representing?
This table is one way to represent the probability distribution for a discrete random variable.
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A table lists the possible number of goals scored in a soccer game and the probability of each. What is this table representing?
This table is one way to represent the probability distribution for a discrete random variable.
What information does interpreting a probability distribution provide?
Interpreting a probability distribution provides information about the shape, center, and spread of a population.
How are the values of a random variable determined?
The values of a random variable are the numerical outcomes that result from random behavior or a random phenomenon.
What is the purpose of interpreting a probability distribution?
The purpose is to gain insights into the characteristics of a population, specifically its shape, center, and spread.
What is the fundamental rule for the probabilities in a discrete probability distribution?
For any discrete random variable, the sum of the probabilities for all possible values must be equal to 1.
Define a discrete random variable.
A discrete random variable is a variable that can take a countable number of values.
What is a cumulative probability distribution?
A cumulative probability distribution shows the probability of a random variable being less than or equal to each specific value.
What three characteristics of a population can be understood from its probability distribution?
The shape, center, and spread of a population can be understood by interpreting its probability distribution.
If X represents the number of defective items in a sample of 5, why is X a discrete random variable?
X is a discrete random variable because it can only take a countable number of values (0, 1, 2, 3, 4, 5).
What are the three common ways to represent a probability distribution?
A probability distribution can be represented by a graph, table, or function.
A probability distribution for a random variable X has P(X=1)=0.2, P(X=2)=0.5, and P(X=3)=0.3. What must be true about the sum of these probabilities?
The sum of the probabilities (0.2 + 0.5 + 0.3) must equal 1, which it does.
What is a random variable?
The values of a random variable are the numerical outcomes of random behavior.
A report shows the probability of a company having 3 or fewer workplace accidents in a year is 0.85. What type of probability is this?
This is a cumulative probability, as it represents the probability of the outcome being less than or equal to a certain value.
A student creates a histogram showing the probabilities of rolling each sum from two six-sided dice. What is this histogram an example of?
This histogram is a graphical representation of a probability distribution.