Workshop in Probability and Statistics

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This workshop will teach you the fundamentals of statistics in order to give you a leg up at work or in school.

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13,783 students enrolled

Current price: $12
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- 21.5 hours on-demand video
- 1 Article
- 14 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

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What Will I Learn?

- By the end of this workshop you should be able to pass any introductory statistics course
- This workshop will teach you probability, sampling, regression, and decision analysis

Requirements

- Knowledge of basic algebra
- Microsoft Excel (recommended)

Description

This workshop is designed to help you make sense of basic probability and statistics with easy-to-understand explanations of all the subject's most important concepts. Whether you are starting from scratch or if you are in a statistics class and struggling with your assigned textbook or lecture material, this workshop was built with you in mind.

Who is the target audience?

- Current students who are (or will soon be) taking a course in introductory statistics with their home institutions
- People in business who want a better grasp of probability and statistics.

Compare to Other Probability Courses

Curriculum For This Course

71 Lectures

22:15:14
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Basic Probability and Terminology
7 Lectures
01:38:13

Basic introduction to probability. Examples using the fundamental probability equation.

Fundamentals of Probability

07:52

Continuing the discussion of basic probability we define complements ("not A") and examine how to find the probability of the complement of an event.

Events and Complements

07:55

More on basic probability. How to find the probability of two or more events occurring when we use the terms "and" and "or." For instance, how to find the probability of events "A and B" / "A or B".

And & Or (Intersection and Union)

18:19

This video provides a brief overview of basic statistical concepts and terms. Defined terms include population vs. sample, mean, median, mode, percentiles, quartiles, geometric mean, variance, standard deviation, Z-scores, and expected values.

Descriptive Statistics

29:17

Problem Set 1

2 pages

Problem Set 1 Walkthrough

25:01

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Joint and Conditional Probability
6 Lectures
01:31:07

How to find the probability of multiple events all taking place when we know the probability of each event.

Preview
18:58

Introduction to conditional probability and how to solve using the fundamental probability equation.

Preview
15:41

Three examples of conditional probability questions solved.

Conditional Probability II

15:53

How to calculate the intersection of several events. More examples using decision trees to calculate probabilities.

Joint and Marginal Probabilities

23:01

Problem Set 2

3 pages

Problem Set 2 Walkthrough

17:34

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Bayes' Rule & Random Variables
7 Lectures
01:35:52

Permutations and Combinations

12:00

Bayes' Theorem and how to solve conditional probability questions using decision trees.

Bayes' Theorem

12:49

Putting it all together with Conditional Probability with a look ahead at Expected Value.

Conditional Probability Challenge Question

17:36

Definition and terms related to random variables and examples of probability distributions, including an explanation of cumulative probability.

Random Variables and Probability Distributions

10:16

Explanation and examples of expected value and its relationship to probability and statistics. Includes a refresher on weighted averages.

Expected Value

15:44

Problem Set 3

3 pages

Problem Set 3 Walkthrough

27:27

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Probability Distributions
5 Lectures
01:23:47

Binomial Distributions

31:42

How to calculate the Expected Value and Standard Deviation of a function when it contains a Random Variable.

Functions of Random Variables

13:32

Graphing probability distributions in an X-Y coordinate plane. Calculating probabilities by measuring the area under a curve. Includes explanations of Histograms and the Uniform Distribution.

Graphing Probability Distributions

09:27

Problem Set 4

3 pages

Problem Set 4 Walkthrough

29:06

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The Normal Distribution
5 Lectures
01:57:06

Introduction to the Normal Distribution and Z Scores. Explanation of how the number of standard deviations from the mean is related to probability.

The Normal Distribution

29:27

How Z Scores (# of standard deviations from the mean of a normal distribution) can be converted to cumulative probabilities. How to use the Standard Normal (Z) Table.

Z-Scores

27:21

In this video we solve several problems related to probabilities and the Normal Distribution. Includes solving for observed values, expected values, standard deviations, and cumulative probabilities.

Z-Score and Normal Distribution Examples

25:15

Problem Set 5

3 pages

Problem Set 5 Walkthrough

35:03

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Joint Random Variables
6 Lectures
01:43:13

How to calculate confidence intervals using the Normal Distribution and Z Scores.

Confidence Intervals

14:03

Definitions, examples, and how to calculate covariances and correlations for two random variables.

Covariance and Correlation of Joint Random Variables

24:55

Portfolio Analysis has to do with how to calculate the joint variance (and standard deviation) of multiple random variables. This video includes the equation to calculate joint variances when there may be multiple instances of two random variable and the variables may be correlated.

Portfolio Analysis

16:18

An example illustrating the concepts of Portfolio Analysis as well as correlation and variance of Joint Random Variables.

Variance in Joint Random Variables Example

18:38

Problem Set 6

3 pages

Problem Set 6 Walkthrough

29:19

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Sampling
7 Lectures
02:14:55

Introduction to Sampling and the Central Limit Theorem. Also how the size of a sample relates to the accuracy of a prediction for a population parameter.

Preview
20:27

More on Sampling and the Central Limit Theorem. How to calculate the probability of observing a sample mean using the standard deviation of the sample.

Sampling Distributions

18:59

How to apply the principles of Sampling and the Central Limit Theorem to proportions. Includes how to calculate a proportion sample standard deviation.

Proportion Sampling

12:11

Definition of the t-distribution an how to perform sampling calculations when the standard deviation of the population is unknown. Also how to use the t-Table.

t-Distributions

20:09

Several examples demonstrating calculations pertaining to Z values, sampling, confidence intervals, proportion sampling, and t-distributions. All related to the previous four videos: Stats 24-27.

Sampling and Confidence Intervals Examples

19:54

Problem Set 7

3 pages

Problem Set 7 Walkthrough

43:15

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Hypothesis Testing
3 Lectures
01:18:53

Introduction to Hypothesis Testing and its relationship to Sampling. How to select null and alternative hypotheses and how to determine whether to use a one-tailed or two-tailed test.

Hypothesis Testing

38:55

Problem Set 8

3 pages

Problem Set 8 Walkthrough

39:58

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Simple Linear Regression
7 Lectures
02:13:09

Introduction to linear regression. Definitions of independent and dependent variables, scatterplots, best-fit lines, residuals, the least-squares method, and the prediction equation.

Simple Linear Regression

18:59

More on simple linear regression including how to analyze the output of regression analysis using example data. Definitions of R-squared, coefficients, and standard errors. Also how to test the significance of the relationship between an independent and dependent variable using hypothesis testing.

Analyzing Regression Output

34:48

A grab bag of additional regression concepts including how to calculate confidence intervals for predicted changes to a dependent variable based on a change to an independent variable, degrees of freedom with multiple independent variables, standardized coefficients, and the F-statistic.

Additional Regression Concepts

15:45

How to calculate confidence intervals for point predictions and population averages using regression.

Prediction and Confidence Intervals in Regression

17:13

Overview of the four main assumptions of linear regression: linearity, independence of errors, homoscedasticity, and normality of residual distribution.

Preview
12:31

Problem Set 9

3 pages

Problem Set 9 Walkthrough

33:53

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Multiple Regression
7 Lectures
02:07:42

Overview of multiple regression including the selection of predictor variables, multicollinearity, adjusted R-squared, and dummy variables.

Multiple Regression (32:23)

32:23

Employing dummy variables and time-lagged variables to come up with a better predictive model for your multiple regression analysis.

Dummy and Time-Lagged Variables

13:45

This video provides a very brief overview of some ways that you can transform your data so that it takes the form of a linear function and can then be used in a regression. Includes exponential and logarithmic transformations.

Transformations

09:39

An example illustrating the iterative process used to select predictor variables for a multiple regression model.

Multiple Regression Case Study

23:39

A quick introduction to ANOVA, including examples of one-way and two-way analysis of variance.

Analysis of Variance (ANOVA)

19:19

Problem Set 10

5 pages

Problem Set 10 Walkthrough

28:57

2 More Sections

About the Instructor