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”

• "Section 1: Discrete Random Variables”
• "Section 2: Probability Distribution Function (PDF) for a Discrete Random Variable”

Instructions: Please read each of the linked sections above in their entirety.

• Lecture: Khan Academy’s Statistics

• “Introduction to Random Variables”
• “Probability Density Functions"

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.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages displayed above.

Expected Value and Standard Deviation

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 4: Discrete Random Variables” :*“Section 3: Mean or Expected Value and Standard Deviation”

Instructions: Please read the entire section in its entirety.

• Lecture: Khan Academy’s Statistics

• “Expected Value: E(X)”

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

Terms of Use: Please respect the copyright and terms of use displayed on the webpage displayed above.

Common Discrete Probability Distributions

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

• “Section 4: Common Discrete Probability Distribution Functions”
• “Section 5: Binomial”
• “Section 6: Geometric (optional)”
• “Section 7: Hypergeometric (optional)”
• “Section 8: Poisson”

Instructions: Please read each of the linked sections above in their entirety.

• 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”

• “Practice 1: Discrete Distribution”
• “Practice 2: Binomial Distribution”
• “Practice 3: Poisson Distribution”
• “Practice 4: Geometric Distribution”
• “Practice 5: Hypergeometric Distribution”

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.

• Lecture: Khan Academy’s Statistics

• “Binomial Distribution 1”
• “Binomial Distribution 2”
• “Binomial Distribution 3”
• “http://www.khanacademy.org/video/binomial-distribution-4?playlist=Statistics Binomial Distribution 4]”

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.

• Lecture: Khan Academy’s Statistics

• “Expected Value of Binomial Distribution”

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.

• Lecture: Khan Academy’s Statistics

• “Poisson Process 1”
• “Poisson Process 2”

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.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.

Subunit 3.2: Continuous Random Variables

Continuous Probability Functions

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

• “Section 1: Continuous Random Variables”
• “Section 2: Continuous Probability Functions”

Instructions: Please read each of the linked sections above in their entirety.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages

Uniform Distribution

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

• “Section 3: The Uniform Distribution”

Instructions: Please read each section above in its entirety.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

Exponential Distribution

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

• “Section 4: The Exponential Distribution”

Instructions: Please read each section above in its entirety.

• 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”

• “Practice 1: Uniform Distribution”
• “Practice 2: Exponential Distribution”

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.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

Subunit 3.3: Normal Distribution

The Standard Normal Distribution

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

• "Section 1: The Normal Distribution”
• “Section 2: The Standard Normal Distribution”

Instructions: Please read each of the linked sections above in their entirety.

• Lecture: Khan Academy’s Statistics

• “Law of Large Numbers”

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

• Lecture: Khan Academy’s Statistics

• “Normal Distribution Excel Exercise”
• “Introduction to Normal Distribution”
• “Normal Distribution Problems: Qualitative Sense of Normal Distributions”

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"

• Section 3: Z-scores”

Instructions: Please read each section above in its entirety.

• Lecture: Khan Academy’s Statistics

• “Normal Distribution Problems: z-score”
• “Normal Distribution Problems: Empirical Rule”
• “Standard Normal Distribution and the Empirical Rule”

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.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

Areas to the Left and Right of x

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

• "Section 4: Areas to the Left and Right of x”

Instructions: Please read each section above in its entirety.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

Calculations of Probabilities

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

• Section 5: Calculations of Probabilities”

Instructions: Please read each section above in its entirety.

• 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”

• “Practice: 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.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

About the Resources in This Course

This course project draws upon three main types of resources:

The first are readings and video lectures from Barbara Illowsky and Susan Dean’s Collaborative Statistics, which is available freely under a Creative Commons Attribution 2.0 Generic (CC BY 2.0) license from the following location: http://cnx.org/content/col10522/latest/

The second type of resources in this course are lectures from Kahn Academy. These lectures are available under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0) license. Kahn Academy has many lectures available from http://www.khanacademy.org/

Finally, the above resources have been woven together and organized into a format analogous to a traditional college-level course by professional consultants that work as experts within the subject area. This process was facilitated by The Saylor Foundation. Additionally, if you have worked through all of the material contained in this project, you may be interested in taking the final exam provided by Saylor.org or completing other courses available there that are not yet on Wikiversity.

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