University Introductory Statistics Discrete Random Variables — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 6 definitions and 7 theorems, 6 worked examples, 2 diagrams, in 13 printable pages. This page lists what the notes cover. The notes themselves come with the University Introductory Statistics bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Discrete Random Variables — what the notes cover
7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Mass functions and cumulative distributions
- Definition — Discrete random variable and its probability mass function
- Definition — Cumulative distribution function
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Expected value
- Definition — Expected value of a discrete random variable
- Theorem — Expected value of a function of a random variable
Also in this section: 1 worked example, 1 note on method and common errors.
Variance and linear transformations
- Definition — Variance and standard deviation
- Theorem — Shortcut formula for the variance
- Theorem — Mean and variance under a linear change of scale
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Bernoulli trials and the binomial formula
- Definition — Bernoulli trial and the binomial model
- Theorem — Binomial probability formula
Also in this section: 1 worked example, 1 note on method and common errors.
Binomial tables, mean and variance
- Theorem — Mean and variance of a binomial variable
- Theorem — Probabilities from a cumulative table
Also in this section: 1 worked example, 1 note on method and common errors.
The Poisson distribution
- Definition — Poisson random variable
- Theorem — Poisson mean, variance and the rate over a new interval
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Introductory Statistics Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Discrete Random Variables practice worksheet is free and stays free.
Every University Introductory Statistics topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Introductory Statistics units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Discrete Random Variables practice worksheet About the Discrete Random Variables unit test