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Learn MoreWorkshop in Probability and Statistics
Rating: 4.6 out of 54.6(4,873 ratings)
35,583 students
Workshop in Probability and Statistics
This workshop will teach you the fundamentals of statistics in order to give you a leg up at work or in school.
Created byGeorge Ingersoll
Last updated 4/2020
English
German [Auto],English
What you'll 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
Explore related topics
Course content
12 sections • 74 lectures • 21h 37m total length
- Fundamentals of Probability8:47
Basic introduction to probability. Examples using the fundamental probability equation.
- Comprehension Check 1.1
- Events and Complements7:21
Continuing the discussion of basic probability we define complements ("not A") and examine how to find the probability of the complement of an event.
- Comprehension Check 1.2
- And (Intersection)7:15
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".
- Comprehension Check 1.3
- Or (Union)8:49
- Comprehension Check 1.4
- Population vs. Sample6:44
Learn how sampling a population enables predictions about the whole, using representative samples and larger sample sizes for more accurate, confident results.
- Measures of Central Tendency12:32
- Comprehension Check 1.5
- Variance & Standard Deviation12:48
Analyze how variance and standard deviation quantify data spread, interpret z-scores and the coefficient of variation, and apply the 68 percent to 95 percent ranges for population and sample data.
- Comprehension Check 1.6
- Expected Value Introduction6:55
Explore expected value as a probabilities-based weighted average, illustrated with GPA and investment examples, showing how to compare opportunities by higher expected value.
- Comprehension Check 1.7
- Problem Set 12:00
- Problem Set 1 Walkthrough25:01
Explore probability fundamentals through problem set 1 walkthrough, including complements, mutually exclusive events, and intersections. Apply expected value, geometric mean, and standard deviation to real scenarios.
- Compound Probability and Independent Events18:58
How to find the probability of multiple events all taking place when we know the probability of each event.
- Comprehension Check 2.1
- Conditional Probability I15:41
Introduction to conditional probability and how to solve using the fundamental probability equation.
- Comprehension Check 2.2
- Conditional Probability II15:53
Three examples of conditional probability questions solved.
- Comprehension Check 2.3
- Joint and Marginal Probabilities23:01
How to calculate the intersection of several events. More examples using decision trees to calculate probabilities.
- Comprehension Check 2.4
- Problem Set 23:00
- Problem Set 2 Walkthrough17:34
- Permutations and Combinations12:00
- Bayes' Theorem12:49
Bayes' Theorem and how to solve conditional probability questions using decision trees.
- Comprehension Check 3.1
- Conditional Probability Challenge Question17:36
Putting it all together with Conditional Probability with a look ahead at Expected Value.
- Random Variables and Probability Distributions10:16
Definition and terms related to random variables and examples of probability distributions, including an explanation of cumulative probability.
- Comprehension Check 3.2
- Expected Value15:44
Explanation and examples of expected value and its relationship to probability and statistics. Includes a refresher on weighted averages.
- Comprehension Check 3.3
- Problem Set 33:00
- Problem Set 3 Walkthrough27:27
- Binomial Distributions31:42
Identify binomial distribution problems with two outcomes, define trials, successes, and probability, and compute exact or range chances. Use the binomial formula, distribution tables, and Excel to apply these concepts.
- Comprehension Check 4.1
- Functions of Random Variables13:32
How to calculate the Expected Value and Standard Deviation of a function when it contains a Random Variable.
- Comprehension Check 4.2
- Graphing Probability Distributions9:27
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.
- Problem Set 43:00
- Problem Set 4 Walkthrough29:06
Explains binomial distributions and complements across problems from elections to quality control, price models, and overbooking. Uses expected value, standard deviation of functions, and Excel for calculations.
- The Normal Distribution29:27
Introduction to the Normal Distribution and Z Scores. Explanation of how the number of standard deviations from the mean is related to probability.
- Comprehension Check 5.1
- Z-Scores27:21
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.
- Comprehension Check 5.2
- Z-Score and Normal Distribution Examples25:15
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.
- Comprehension Check 5.3
- Problem Set 53:00
- Problem Set 5 Walkthrough35:03
- Confidence Intervals14:03
How to calculate confidence intervals using the Normal Distribution and Z Scores.
- Comprehension Check 6.1
- Covariance and Correlation of Joint Random Variables24:55
Definitions, examples, and how to calculate covariances and correlations for two random variables.
- Comprehension Check 6.2
- Portfolio Analysis16:18
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.
- Comprehension Check 6.3
- Variance in Joint Random Variables Example18:38
An example illustrating the concepts of Portfolio Analysis as well as correlation and variance of Joint Random Variables.
- Problem Set 63:00
- Problem Set 6 Walkthrough29:19
Explore applying normal distribution to real data: compute 99% and 95% confidence intervals, assess probabilities for ranges, and derive portfolio variance and correlations from joint variables.
- Sampling20:27
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.
- Sampling Distributions18:59
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.
- Comprehension Check 7.1
- Proportion Sampling12:11
How to apply the principles of Sampling and the Central Limit Theorem to proportions. Includes how to calculate a proportion sample standard deviation.
- Comprehension Check 7.2
- t-Distributions20:09
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.
- Comprehension Check 7.3
- Sampling and Confidence Intervals Examples19:54
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.
- Comprehension Check 7.4
- Problem Set 73:00
- Problem Set 7 Walkthrough43:15
- Hypothesis Testing38:55
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.
- Comprehension Check 8.1
- Problem Set 83:00
- Problem Set 8 Walkthrough39:58
- Simple Linear Regression18:59
Introduction to linear regression. Definitions of independent and dependent variables, scatterplots, best-fit lines, residuals, the least-squares method, and the prediction equation.
- Analyzing Regression Output34:48
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.
- Additional Regression Concepts15:45
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.
- Prediction and Confidence Intervals in Regression17:13
How to calculate confidence intervals for point predictions and population averages using regression.
- Regression Assumptions12:31
Overview of the four main assumptions of linear regression: linearity, independence of errors, homoscedasticity, and normality of residual distribution.
- Problem Set 93:00
- Problem Set 9 Walkthrough33:53
Walk through a simple linear regression analyzing entree price as a predictor of alcohol sales per customer, covering correlation, two-tailed tests, and confidence and prediction intervals.
- Multiple Regression (32:23)32:23
Overview of multiple regression including the selection of predictor variables, multicollinearity, adjusted R-squared, and dummy variables.
- Dummy and Time-Lagged Variables13:45
Employing dummy variables and time-lagged variables to come up with a better predictive model for your multiple regression analysis.
- Transformations9:39
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.
- Multiple Regression Case Study23:39
An example illustrating the iterative process used to select predictor variables for a multiple regression model.
- Analysis of Variance (ANOVA)19:19
A quick introduction to ANOVA, including examples of one-way and two-way analysis of variance.
- Problem Set 105:00
- Problem Set 10 Walkthrough28:57
Analyze a two-predictor multiple regression for final exam scores, interpret coefficients, confidence intervals, and hypothesis tests, and assess model improvements with extra predictors and dummy variables.
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 this course is for:
- 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.