Lecture 5

Instructor

Jeremy Jackson

| May 5, 2020

Location:

NW 3428

| New Westminster

Sir Ken Robinson: "Learning happens in the minds and souls, not in the databases of multiple-choice tests"

**Text Font Conventions**

- You will be responsible for knowing a number of definitions of key concepts. You may be asked to give an accurate definition and example of any of the key concepts. Key concepts are in italics, bolded and colored red throughout the notes.Key conceptsCritical points - There are some points that require extra emphasis because they are fundamental to the example or concept being discussed. Critical points are bolded, in italics and colored orange.

- These are the questions given in the learning objectives document.Course learning objective questions

**Lecture 5**

This week, we take a look at a different class of distribution. So far, we have looked at empirical distributions, that is distributions of real-world occurrences of some phenomenon. In particular, we have focused mostly on the distribution of the frequency with which something occurs in the world. This week, we start looking at theoretical distributions. That is, mathematical distributions. These are distributions that are made up by statisticians generally to be used as models for empirical distributions. By the time you have watched and taken notes on the videos in this lecture, you should be able to address learning objectives question 15 - Describe the difference between a probability distribution and a probability density function. So let's start with an introductory video on the difference between empirical and theoretical distributions.

1) Empirical vs theoretical distributions....here

Now watch the two technical videos on probability functions and probability density functions. Go ahead a watch the videos now...

2) Probability functions technical video....here

3) Probability density functions technical video....here

It's important to understand how these distributions are used as models of empirical distributions. The following videos describe this issue.

4) How we use probability functions....here

5) How we use probability density functions....here

Now let's take a look at the most common theoretical distribution we will use in this course...the Normal Distribution.

6) The Normal Distribution technical video....here

Now let's take a look at a very typical type of error that people make when they do not properly understand the difference between empirical and theoretical distributions. In this course, you will need to know and understand the difference and how to speak properly about empirical and theoretical distributions.

7) Are IQ scores Normally Distributed....here

By the time you have watched and taken notes on the videos above and worked to understand them and commit to memory the names, definitions and symbols associated with each concept, you should understand what a theoretical distribution is, how it differs from an empirical distribution and how theoretical distributions are used to calculate probabilities.

Now, let's just go over some examples of calculating probabilities of events for various different kinds of probability functions and probability density functions.

8) Calculating probabilities examples....here

That's it for this week. Feel free to ask questions on the "Course Questions" discussion board in Blackboard. I will answer questions on Tuesdays and Thursdays of each week.

Now on to lecture 6.