# Introduction to Statistical Analysis/Unit 3 Content

## Unit 3

This content is adapted from the Introduction to Statistics MA121/ECON104 Course at Saylor.org.

### Subunit 3.1: Discrete Random Variables and Discrete Probability Distributions

#### Probability Distribution Functions

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 4: Discrete Random Variables”

Instructions: Please view the linked lecture titled “Introduction to Random Variables” (12:04 minutes). This lecture will provide an introduction to random variables and probability distribution functions. Then, view the “Probability Density Functions” lecture (10:02 minutes) to learn about probability density functions for continuous random variables.

#### Expected Value and Standard Deviation

Instructions: Please view the lecture in its entirety (approximately 15 minutes). In this lecture, you will learn about how to calculate expected value.

#### Common Discrete Probability Distributions

Play media
Video Lecture: Discrete Distributions
• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 4: Discrete Random Variables”

• Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: Video Lecture 4: Discrete Distributions.

Instructions: Please view the lecture to the right in its entirety.

• Assignment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 4: Discrete Random Variables”

Instructions: Click on the hyperlinks titled “Practice 1: Discrete Distribution,” “Practice 2: Binomial Distribution,” “Practice 3: Poisson Distribution,” “Practice 4: Geometric Distribution,” and “Practice 5: Hypergeometric Distribution” and solve all the problems in these sections. Next, click on the hyperlink titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31. Please click on the “[ Show Solution ]” link below the problem to check your solution.

Instructions: Please view all four lectures in their entirety (approximately 47 minutes total). In the first three lectures, you will learn about the binomial distribution. In the fourth lecture, you will learn to use excel to visualize the basketball binomial distribution presented in the third video.

Instructions: Please view the lecture in its entirety (approximately 17 minutes). In this lecture, you will learn about the expected value of a binomial distributed random variable.

Instructions: Please view the both lectures in their entirety (approximately 24 minutes total). In these lectures, you will learn about the Poisson processes and the Poisson distribution as well as the derivation of the Poisson distribution.

### Subunit 3.2: Continuous Random Variables

#### Continuous Probability Functions

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 5: Continuous Random Variables”

#### Uniform Distribution

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 5: Continuous Random Variables”

#### Exponential Distribution

Play media
Video Lecture 5: Continuous Random Variables
• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 5: Continuous Random Variables”

• Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 5: Continuous Random Variables”

Instructions: Please view the lecture to the right.

• Assignment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 5: Continuous Random Variables”

Instructions: Click on the hyperlinks titled “Practice 1: Uniform Distribution,” “Practice 2: Exponential Distribution.” Please solve all the problems in these two sections. Next, click on the hyperlink titled “Homework” and solve problems 3, 5, 7, 9, 11, 13, 15-20. The solutions are provided below the problem. Please solve all of the problems before checking the solutions.

### Subunit 3.3: Normal Distribution

#### The Standard Normal Distribution

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 6: The Normal Distribution"

Instructions: Please view the lecture in its entirety (9:00 minutes). In this lecture, you will learn about the law of large numbers.

Instructions: Please view the lectures linked above. In the lecture titled “Normal Distribution Excel Exercise” (26 minutes), you will see a presentation on a spreadsheet, which will show that the normal distribution approximates the binomial distribution for a large number of trials. Please view the other two lectures on normal distribution in their entirety (approximately 37 minutes total).

#### Z-scores

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 6: The Normal Distribution"

Instructions: Please view the three lectures in their entirety (approximately 26 minutes total). In these lecture, you will learn about the z-scores and how to use the empirical rule (the 68-95-99.7 rule) to estimate probabilities for normal distributions.

#### Areas to the Left and Right of x

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 6: The Normal Distribution"

#### Calculations of Probabilities

Play media
Video Lecture 6: The Normal Distribution
• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 6: The Normal Distribution"

• Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 6: The Normal Distribution”

Instructions: Please view the lecture to the right in its entirety.

• Assignment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 6: The Normal Distribution”

Instructions: Click on the hyperlink titled “Practice: The Normal Distribution”. Please solve all the problems in this section. Next, click on the hyperlink titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 12-19. The solutions are provided below the problem. Please solve all of the problems before checking the solutions.