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Boundless Statistics
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Chapter 9

Probability and Variability

Book Version 1
By Boundless
Boundless Statistics
Statistics
by Boundless
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Section 1
Discrete Random Variables
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Two Types of Random Variables

A random variable xxx, and its distribution, can be discrete or continuous.

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Probability Distributions for Discrete Random Variables

Probability distributions for discrete random variables can be displayed as a formula, in a table, or in a graph.

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Expected Values of Discrete Random Variables

The expected value of a random variable is the weighted average of all possible values that this random variable can take on.

Section 2
The Binomial Random Variable
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The Binomial Formula

The binomial distribution is a discrete probability distribution of the successes in a sequence of nnn independent yes/no experiments.

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Binomial Probability Distributions

This chapter explores Bernoulli experiments and the probability distributions of binomial random variables.

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Mean, Variance, and Standard Deviation of the Binomial Distribution

In this section, we'll examine the mean, variance, and standard deviation of the binomial distribution.

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Additional Properties of the Binomial Distribution

In this section, we'll look at the median, mode, and covariance of the binomial distribution.

Section 3
Other Random Variables
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The Poisson Random Variable

The Poisson random variable is a discrete random variable that counts the number of times a certain event will occur in a specific interval.

The Hypergeometric Random Variable

A hypergeometric random variable is a discrete random variable characterized by a fixed number of trials with differing probabilities of success.

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Boundless Statistics by Boundless
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Probability
  • What Are the Chances?
  • Probability Rules
  • More About Chance
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Chapter 9
Probability and Variability
  • Discrete Random Variables
  • The Binomial Random Variable
  • Other Random Variables
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Chapter 10
Continuous Random Variables
  • The Normal Curve
  • Normal Approximation
  • Measurement Error
  • Expected Value and Standard Error
  • Normal Approximation for Probability Histograms
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