Chapter 4 Wrap-Up
Concept Check
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Section Resources
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4.1 Introduction to Probability and Random Variables
4.4 Continuous Random Variables
4.6 The Normal Approximation to the Binomial
Key Terms
Try to define the terms below on your own. Check your response by clicking on the term, or looking at the end-of-book glossary!
4.1 Introduction to Probability and Random Variables
- Probability
- Probability experiment
- Outcome
- Sample space
- Event
- Probability model
- Law of large numbers
- Complement
4.2 Discrete Random Variables
- Discrete random variable
- Probability mass function (PMF)
- Cumulative distribution function (CDF)
- Expected value
4.3 The Binomial Distribution
4.4 Continuous Random Variables
4.5 The Normal Distribution
4.6 The Normal Approximation to the Binomial
Extra Practice
Extra practice problems are available at the end of the book (Chapter 4 Extra Practice).
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
An outcome or subset of outcomes of an experiment in which you are interested
A mathematical representation of a random process that lists all possible outcomes and assigns probabilities to each
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 random variable that takes on a countable amount 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 random variable (RV) whose outcomes are measured as an uncountable, infinite number of values
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, and continuous probability distribution
Roughly 68% of values are within one standard deviation of the mean, roughly 95% of values are within two standard deviations of the mean, and 99.7% of values are within three 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