Workshop in Probability and Statistics
Categories:
Academics
This workshop is designed to help you make sense of basic probability and statistics with easytounderstand 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.
Course Details
Basic Probability and Terminology 
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Course Welcome/ Introductory Lecture 
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Fundamentals of Probability 
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<p style=""> Basic introduction to probability. Examples using the fundamental probability equation. </p> 
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Events and Complements 
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<p style=""> Continuing the discussion of basic probability we define complements ("not A") and examine how to find the probability of the complement of an event. </p> 
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And & Or (Intersection and Union) 
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<p style=""> 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". </p> 
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Descriptive Statistics 
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<p style=""> 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, Zscores, and expected values. </p> 
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Problem Set 1 
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Problem Set 1 Walkthrough 
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Joint and Conditional Probability 
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Compound Probability and Independent Events 
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<p style=""> How to find the probability of multiple events all taking place when we know the probability of each event. </p> 
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Conditional Probability I 
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<p style=""> Introduction to conditional probability and how to solve using the fundamental probability equation. </p> 
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Conditional Probability II 
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<p style=""> Three examples of conditional probability questions solved. </p> 
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Joint and Marginal Probabilities 
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<p style=""> How to calculate the intersection of several events. More examples using decision trees to calculate probabilities. </p> 
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Problem Set 2 
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Problem Set 2 Walkthrough 
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Bayes' Rule & Random Variables 
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Permutations and Combinations 
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Bayes' Theorem 
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<p style=""> Bayes' Theorem and how to solve conditional probability questions using decision trees. </p> 
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Conditional Probability Challenge Question 
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<p style=""> Putting it all together with Conditional Probability with a look ahead at Expected Value. </p> 
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Random Variables and Probability Distributions 
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<p style=""> Definition and terms related to random variables and examples of probability distributions, including an explanation of cumulative probability. </p> 
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Expected Value 
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<p style=""> Explanation and examples of expected value and its relationship to probability and statistics. Includes a refresher on weighted averages. </p> 
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Problem Set 3 
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Problem Set 3 Walkthrough 
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Probability Distributions 
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Binomial Distributions 
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<p style=""> Introduction to Binomial Distributions. How to find binomial probabilities using equations, Excel, and Binomial Tables. </p> <p style=""> <em style="">Correction (29:4529:52): Using the binomial table you would subtract the value for x<=<strong style="">329</strong> (not 330)</em> </p> 
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Functions of Random Variables 
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<p style=""> How to calculate the Expected Value and Standard Deviation of a function when it contains a Random Variable. </p> 
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Graphing Probability Distributions 
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<p style=""> Graphing probability distributions in an XY coordinate plane. Calculating probabilities by measuring the area under a curve. Includes explanations of Histograms and the Uniform Distribution. </p> 
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Problem Set 4 
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Problem Set 4 Walkthrough 
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The Normal Distribution 
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The Normal Distribution 
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<p style=""> Introduction to the Normal Distribution and Z Scores. Explanation of how the number of standard deviations from the mean is related to probability. </p> 
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ZScores 
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<p style=""> 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. </p> 
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ZScore and Normal Distribution Examples 
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<p style=""> 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. </p> 
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Problem Set 5 
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Problem Set 5 Walkthrough 
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Joint Random Variables 
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Confidence Intervals 
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<p style=""> How to calculate confidence intervals using the Normal Distribution and Z Scores. </p> 
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Covariance and Correlation of Joint Random Variables 
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<p style=""> Definitions, examples, and how to calculate covariances and correlations for two random variables. </p> 
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Portfolio Analysis 
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<p style=""> 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. </p> 
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Variance in Joint Random Variables Example 
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<p style=""> An example illustrating the concepts of Portfolio Analysis as well as correlation and variance of Joint Random Variables. </p> 
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Problem Set 6 
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Problem Set 6 Walkthrough 
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Sampling 
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Sampling 
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<p style=""> 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. </p> 
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Sampling Distributions 
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<p style=""> 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. </p> 
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Proportion Sampling 
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<p style=""> How to apply the principles of Sampling and the Central Limit Theorem to proportions. Includes how to calculate a proportion sample standard deviation. </p> 
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tDistributions 
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<p style=""> Definition of the tdistribution an how to perform sampling calculations when the standard deviation of the population is unknown. Also how to use the tTable. </p> 
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Problem Set 7 
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Problem Set 7 Walkthrough 
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Hypothesis Testing 
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Sampling and Confidence Intervals Examples 
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<p style=""> Several examples demonstrating calculations pertaining to Z values, sampling, confidence intervals, proportion sampling, and tdistributions. All related to the previous four videos: Stats 2427. </p> 
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Hypothesis Testing 
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<p style=""> Introduction to Hypothesis Testing and its relationship to Sampling. How to select null and alternative hypotheses and how to determine whether to use a onetailed or twotailed test. </p> 
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Problem Set 8 
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Problem Set 8 Walkthrough 
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Simple Linear Regression 
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Simple Linear Regression 
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<p style=""> Introduction to linear regression. Definitions of independent and dependent variables, scatterplots, bestfit lines, residuals, the leastsquares method, and the prediction equation. </p> 
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Analyzing Regression Output 
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<p style=""> More on simple linear regression including how to analyze the output of regression analysis using example data. Definitions of Rsquared, coefficients, and standard errors. Also how to test the significance of the relationship between an independent and dependent variable using hypothesis testing. </p> 
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Additional Regression Concepts 
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<p style=""> 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 Fstatistic. </p> 
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Prediction and Confidence Intervals in Regression 
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<p style=""> How to calculate confidence intervals for point predictions and population averages using regression. </p> 
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Regression Assumptions 
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<p style=""> Overview of the four main assumptions of linear regression: linearity, independence of errors, homoscedasticity, and normality of residual distribution. </p> 
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Problem Set 9 
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Problem Set 9 Walkthrough 
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Multiple Regression 
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Multiple Regression (32:23) 
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<p style=""> Overview of multiple regression including the selection of predictor variables, multicollinearity, adjusted Rsquared, and dummy variables. </p> 
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Dummy and TimeLagged Variables 
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<p style=""> Employing dummy variables and timelagged variables to come up with a better predictive model for your multiple regression analysis. </p> 
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Transformations 
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<p style=""> 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. </p> 
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Multiple Regression Case Study 
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<p style=""> An example illustrating the iterative process used to select predictor variables for a multiple regression model. </p> 
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Analysis of Variance (ANOVA) 
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<p style=""> A quick introduction to ANOVA, including examples of oneway and twoway analysis of variance. </p> 
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Problem Set 10 
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Problem Set 10 Walkthrough 
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Decision Analysis 
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Decision Analysis I: Decision Trees 
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<p style=""> Steps for creating complex decision trees to aid in decision analysis using chance nodes and decision nodes. </p> 
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Decision Analysis II: The Value of Information 
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<p style=""> More on decision analysis including how to calculate the value of information. </p> 
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Problem Set 11 
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Problem Set 11 Walkthrough 
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Concluding Lecture 
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Made a perfectly clear demonstration of a formulaic representation, making the information very accessible.
Good course. Great instruction.
seem clear and fun.
Looks good! I need much help in my MBA Statistics class and this looks to be just the ticket!!! Thanks George!
Nothing to improve, in my humble opinion. I'm still at the beginning and I'm not bored, so far.
The lectures are great and the problem sets really get you thinking. Good stuff.
I'm not far in the course yet, but I really like what I've learned so far, and I can tell the course is only going to get better as he begins to discuss more advanced and complex concepts. He has a wonderful way of simplifying difficult concepts and using key samples for clarification. This course is definitely worth the small investment.
good
Better than average
Engaging, interesting, well worth the time
He makes understanding the concepts very easy !