A distribution from a sample space

Construct theoretical discrete distributions and compute their expectations

Problem types

Defining a random variable
Using expected value to compare choices
The multiplication rule for probability · Earlier idea
Multiplying the probabilities along a sequence of trials gives the probabilities in a theoretical distribution.
The binomial theorem · Useful idea
The probability of k successes in n independent trials with success chance p is C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ. These are the terms of the expansion of (p + (1 − p))ⁿ, which sum to 1.
Permutations and combinations · Useful idea
Counting arrangements gives the numbers of ways behind binomial and other theoretical probabilities.
The normal distribution · Earlier idea
A normal distribution is a theoretical distribution with a mean and standard deviation, as a discrete distribution has an expected value.

Comparing uncertain strategies · See it applied
Expected values computed from a theoretical distribution are the averages used to compare uncertain choices.
Margin of error and what a sample supports · Extend the idea
A theoretical distribution of sample means gives the margin of error used in statistical inference.

A procedure that gives each outcome a fair chance · Related idea
A fair procedure has a theoretical distribution in which every outcome is equally likely.
A distribution built from frequencies · Shared foundations

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