Chapter 4 Wrap Up
Concept Check
Section Resources
4.1 Introduction to Probability and Random Variables
4.4 Continuous Random Variables
Key Terms
Try to define the terms below on your own. Scroll over any term to check your response!
4.1 Introduction
- Probability
- Probability experiment
- Outcome
- Sample space
- Event
- Probability model
- Law of large numbers
- Complement
4.2 Introduction to DRVs
- Random variable
- Probability model
- Discrete random variable
- Continuous random variable
- Probability mass function (PMF)
- Cumulative distribution function (CDF)
- Expected value
4.3 The Binomial Distribution
- Discrete random variable
- Binomial experiment
- Independent
- Bernoulli trial
- Probability mass function
- Cumulative distribution function
4.4 Introduction to CRVs
- Continuous random variable
- Probability density function (PDF)
- Cumulative distribution function (CDF)
- Uniform distribution
4.5 Normal Distribution
- Normal (Gaussian) distribution
- Probability density function (PDF)
- Empirical rule
- Standard normal distribution (SND)
- Z-score
- Quantile
4.6 Normal Approximation to the Binomial
Extra Practice
Link to Chapter 4 Extra Practice Problems
The study of randomness; a number between zero and one, inclusive, that gives the likelihood that a specific event will occur
A random experiment where the result is not predetermined
A particular result of an experiment
The set of all possible outcomes of an experiment
A single outcome, or subset of outcomes, of an experiment that you are interested in
A mathematical representation of a random process that lists all possible outcomes and assigns probabilities to each of them
As the number of trials in a probability experiment increases, the relative frequency of an event approaches the theoretical probability
The complement of an event consists of all outcomes in a sample space that are NOT in the event
A representation of a probability model
A random variable that produces discrete data
A random variable (RV) whose outcomes are measured as an uncountable, infinite, number of values
A function that gives the probability that a discrete random variable is exactly equal to some value (x)
A function that gives the probability that a random variable takes a value less than or equal to x
Mean of a random variable
A random variable that counts the number of successes in a fixed number (n) of independent Bernoulli trials each with probability of a success (p)
The occurrence of one event has no effect on the probability of the occurrence of another event
An experiment with the following characteristics:
- There are only two possible outcomes called “success” and “failure” for each trial
- The probability (p) of a success is the same for any trial (so the probability q = 1 − p of a failure is the same for any trial)
A function that defines a continuous random variable, and the likelihood of an outcome
A probability distribution in which all outcomes are equally likely
A commonly used symmetric, unimodal, bell-shaped, continuous probability distribution
Roughly 68% of values are within 1 standard deviation of the mean, roughly 95% of values are within 2 standard deviations of the mean, and 99.7% of values are within 3 standard deviations of the mean
A normal random variable with a mean of 0 and standard deviation of 1 which z-scores follow; denoted N(0, 1)
A measure of location that tells us how many standard deviations a value is above or below the mean
Points in a distribution that relate to the rank order of values in that distribution
When statisticians add or subtract .5 to values to improve approximation