At its most basic, statistics uses a sample of data to draw conclusions about the population that gave us that data. This necessitates a bridge between the sample and the population. Probability serves as that bridge.
In this part, we examine probability from its basic rules to different types of probability distributions. Through it all, understanding probability is important to understanding how we can draw conclusions about a population based on a sample.
Learning Objectives
As you work your way through this part of the course, make sure you are able to…
- calculate probabilities from given information;
- write the probability mass function from a description;
- determine if a randm variable is discrete or continuous;
- determine which named distribution best matches observed data;
- state examples of Binomial, Poisson, Hypergeometric, Uniform, Exponential, and Normal random variables;
- understand the importance of the Central Limit Theorem to statistics; and
- calculate sampling distributions (approximate and exact).
Reading Assignments
In your textbook, make sure you carefully read and take notes on the following sections:
- Chapter 4: 1–6
- Chapter 5: 1–6, Appendix 5.1
- Chapter 6: 1–6, Appendix 6.1
- Chapter 7: 1–3
Remember that the chapter appendices give you an introduction to performing these calculations in Excel.
Supplemental Materials
While I have no lecture on this topic, there is some practice available to you at Project Scarlet on this learning objective. Make sure you use this enough times so that you can calculate the mean, the variance, and the probabilities for any discrete distribution. This topic is also covered in Section 6.1 in the text.
The Binomial Distribution. This gives you three things. First, it covers the Binomial distribution. Second, it introduces you to the incredible resource that is Khan Academy. Third, it gives you a few videos that may help with understanding the Binomial distribution. While the Binomial distribution is optional (Section 6.2), it is helpful in understanding all of our future work with proportions.
The Uniform Distribution. The most basic of continuous distributions is the Uniform distribution. Each outcome is equally likely. Probabilities, always calculated as areas, can be calculated here using simple geometry. This quick lecture continues your introduction to the Uniform distributions.
The Normal Distribution. Arguably, the most important distribution in all statistics is the Normal distribution. In this mini-lecture, I show you how to calculate probabilities using the standard Normal table as well as using StatCrunch and Excel.
The Central Limit Theorem. The most important theorem in all probability is the Central Limit Theorem. Its statement is easy. Its consequences are far-reaching. In this mini-lecture, I cover the Central Limit Theorem and sampling distributions.
The GM Recall. In this lengthy series of examples, we apply the Binomial distribution and the Normal distribution to a real-life problem faced by many businesses: How many replacement parts should be bought? Here, it is ignition switches, but the ideas apply to any business with inventory.
It may be best if you view this video at the start and at the end of this part. Viewing it at the start should give you context to why a lot of these techniques will be useful. Viewing it at the end reminds you of all you did in these three chapters.