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 Probability and Statistics Video Series15 Videos(Single Video $40.00/each. See below for individual purchase.) |
This Probability and Statistics video tutor series consists of 15 tapes containing 60 half-hour segments. The objective of this series is to give the student a resource in probability and statistics. The approach we used is to cover all the topics of the standard two semester course in Probability and Statistics, one topic per segment. For each segment, the basic set-up and theoretical framework is reviewed and then examples are worked illustrating the theory. Word problems of a realistic nature are emphasized throughout.
The topics covered include frequency distributions, measures of central tendency of data such as the mean, and standard deviation, probability and conditional probability, random variables and expectations, binomial, normal, and Poisson distributions, confidence intervals, hypothesis tests, regression and correlation, goodness of fit, testing for normality, and analysis of variance.
Video 1 - Populations and Data, Frequency, Mean
- Populations and Data.
This segment is an introductory discussion about what problems statisticians deal with, and the notion of population as distinct from data. - Frequency distributions.
This segment is about grouping numerical data into classes, frequency, relative frequency, density, real class intervals, real class boundaries, real class midpoints, guidelines for choosing classes.
- Visual Display of Data.
This segment covers histograms, frequency polygons, cumulative distributions and ogives, and pie graphs.
- Mean.
This segment covers the formulas for the mean of a sample and of a population and examples illustrating their computation.
Video 2 - Mode, Median, Means, Variance, Standard Deviation
- Mode, Median, and Midrange.
This segment covers the definition and computation of modes, medians, and midranges for data and for populations.
- Means, Medians, and Modes of Grouped Data.
This segment covers the estimation and computation of means, medians, and modes of grouped data such as from frequency, relative frequency, and density histograms for data and for populations.
- Variance and Standard Deviation.
This segment covers the formulas and computations of variance and standard deviation of populations, samples, and grouped data, emphasizing mean of square minus square of mean.
- Sample Spaces and Events.
This segment covers the basic notions for setting up probability theory, the notions of outcome, sample space, and event.
Video 3 - Probability, Gambling Odds, Independent Events
- Probability Laws and Gambling Odds.
This segment covers the basic laws of probability, the relationship between mathematical probability and gambling odds, and elementary computations with laws of n probability, as well as the notion of mutually exclusive events.
- Model of Equally Likely Outcomes.
This segment covers the definition and basic examples and applications of the model of equally likely outcomes for computing probability.
- Conditional Probability.
This segment covers the definition and applications of conditional probability.
- Independent Events.
This segment covers the definition of independence for events, equivalent formulations for detecting independence and comparison with notion of mutual exclusivity.
Video 4 - Bayes Theorem, Permutations & Factorials
- Bayes Theorem.
This segment covers the result known as Bayes Theorem for computation of certain conditional probabilities using a partition of the sample space, as well as applications.
- Multiplication Principle for Counting.
This segment covers the multiplication principle for counting the outcomes for multi-stage processes where the number of outcomes at each stage is independent of the particular history of outcomes of previous stages. Applications of the multiplication principle to typical counting problems are given.
- Permutations and Factorials.
This segment covers computations with permutations and factorial notation for counting permutations as well as applications to probability.
- Combinations.
This segment covers the definitions of combinations, binomial coefficients, Pascal's triangle, and applications to probability.
Video 5 - Random Variables & Distributions
- Random Variables and Distributions.
This segment covers the basic definitions of function, of random variable as real-valued function on sample space, of distribution of a random variable and examples.
- Continuous Random Variables and Densities.
This segment covers the notion of continuous random variable and the use of density to describe its distribution, as well as illustrative examples.
- Expectations of Random Variables.
This segment covers the definition and computation of the expected value of a random variable as well as the rules for computation of expected values of sums and constant multiples of random variables, the linearity of expectation.
- Variance of Random Variables.
This segment covers the definition of the variance of a random variable as the expected value of the squared deviation from the mean and the equivalence with the expected value of the square minus the square of the expected value as well as the use of the latter in computations.
Video 6 - Binomial Distribution, Poisson Distribution
- Independent Random Variables.
This segment covers the definition and basic rules for the computation of expected value of a product of independent random variables, the variance of the sum of independent random variables, and applications.
- Binomial Distribution.
This segment covers the definition and the basic applications of the binomial distribution to problems of repeated independent trials of a two-outcome experiment.
- Poisson distribution.
This segment covers the definition and applications of the Poisson distribution.
- Tchebychev's Approximation.
This segment covers the inequality known as Tchebychev's approximation and applications to random variables with unknown distribution.
Video 7 - Normal Distribution, Central Limit Theorem
- Normal Distribution and Standardization.
This segment covers the definition of the normal distribution, the method of standardization of a normal random variable for determining its distribution from the tabulated Z-distribution, the standard normal random variable.
- Central Limit Theorem.
This segment covers the central limit theorem on limit in mean of a sequence of identically distributed random variables being normally distributed as well as generally accepted criterion for using the normal approximation in applications.
- Normal Approximation to Binomial.
This segment covers the criterion and applications for approximating the binomial distribution by the normal distribution.
- Sampling Distribution of Mean.
This segment covers the notion of the sample mean as a random variable and its expected value.
Video 8 - Standard Error, Confidence Interval, T-Distribution
- Standard Error of Mean.
This segment covers the standard error of the mean as the variance of the sample mean as a random variable, as well as computational examples.
- Confidence Intervals with Variance Known.
This segment covers the construction of confidence intervals for the mean of a random variable in cases where the variance of the random variable is known, and where a sample mean and the standard Z-distribution can be applied.
- T-Distribution and Confidence Intervals.
This segment covers the construction of confidence intervals for the mean of a normal random variable in cases where the sample mean, the sample variance, and the T-distribution are required.
- Confidence Intervals for Proportions.
This segment covers the use of the normal approximation to the binomial for constructing confidence intervals for a proportion using sample data and the standard Z-distribution.
Video 9 - Hypothesis Test, Confidence Intervals, Chi-Square
- Confidence Intervals for Variance and Chi-Square.
This segment covers sample variance as a random variable, standardization of sample variance, the chi-square distribution and applications to confidence intervals for variance and standard deviation.
- Hypothesis Testing.
This segment covers the basic notions of a hypothesis test, the Type I and Type II errors, the notion of level of significance and null hypothesis, and power, as well as comparison with scientific method and legal trial. Emphasis here is on developing understanding of the basic logical set up and framework for hypothesis testing in general, and use the fact that the alternate hypothesis is the only hypothesis which can be proved as a guide to setting up hypothesis tests..
- Hypothesis Tests About Mean.
This segment covers the basic maximum power tests for null hypotheses which are inequalities or equalities involving the mean of an unknown population, when to use the Z-distribution.
- Hypothesis Tests With Variance Unknown.
This segment covers hypothesis tests of inequalities or equalities involving the mean using the T-distribution in the case the population varia.
Video 10 - Hypothesis Tests of Proportions, Variance & Means
- Hypothesis Tests of Proportions.
This segment covers hypothesis tests of inequalities or equalities involving variance of standard deviation using sample data and the chi-square distribution.
- Hypothesis Tests of Variance.
This segment covers hypothesis tests of inequalities or equalities involving variance of standard deviation using sample data and the chi-square distribution.
- Confidence Intervals for Difference of Means.
This segment covers the methods for constructing a confidence interval for the difference of means of two different populations.
- Hypothesis Tests for Difference of Means.
This segment covers the hypothesis tests and methods of dealing with equalities and inequalities of means of two different populations.
Video 11 - Confidence Intervals and Hypothesis Tests
- Confidence Intervals & Hypothesis Tests I.
This segment covers tests and confidence intervals for the difference of two means in case the variances are unknown, using pooled variance in cases the variances can be assumed equal and the formula for degrees of freedom to compensate if variances cannot be assumed equal.
- Confidence Intervals & Hypothesis Tests II.
This segment covers confidence intervals and hypothesis tests for the difference of two proportions.
- Confidence Intervals & Hypothesis Tests III.
This segment covers confidence intervals and hypothesis tests concerning the difference in two related populations.
- Confidence Intervals & Hypothesis Tests IV.
This segment covers hypothesis tests and confidence intervals for comparing variances of two independent normal populations using the F-distribution.
Video 12 - Linear Regression, Coefficient of Correlation
- Linear Regression.
This segment covers scatter diagrams and the least-squares best fitting straight line relating two variables.
- Coefficient of Correlation.
This segment covers the computation of the sample correlation coefficient and its use in the hypothesis test for independence of two random variables.
- Standard Error of Regression.
This segment covers the standard error of the regression line and the confidence intervals for the regression slope and vertical intercept, as well as the confidence interval for the variance in the regression error.
- Prediction Intervals.
This segment covers the confidence intervals for single observation on the regression line.
Video 13 - Normality, Predictive Association, Goodness of Fit
- Goodness of Fit.
This segment covers the Pearson chi-squared statistic and its use in testing hypothetical categorical models.
- Normality Test.
This segment covers the goodness of fit test as applied to testing for normality in a population.
- Two Variance Goodness of Fit and Independence.
This segment covers the goodness of fit test as applied to testing for independence of two classifications.
- Index of Predictive Association.
This segment covers the use of the index of predictive association as a measure of dependence of two attributes.
Video 14 - One and Two Way Analysis of Variance, Sign Test
- One-Way Analysis of Variance.
This segment covers one-way analysis of variance of normal populations and the related hypothesis test for equality of means using the F-distribution.
- Two-Way Analysis of Variance I.
This segment covers the simultaneous hypothesis tests for two-way classification using one observation per cell.
- Two-Way Analysis of Variance II.
This segment covers two-way analysis of variance in the case of multiple observations per cell.
- Sign Test.
This segment covers the one-sample sign test for hypothesis about the median of a possibly non-normal population.
Video 15 - Runs & Rank Tests, Spearman Rand Correlation
- Two-Sample Sign Test.
This segment covers the two-sample sign test for differences.
- Runs Test.
This segment covers the runs test for randomness and its applications.
- Rank Tests.
This segment covers the Mann-Whitney rank test and the Wilcoxon signed rank test.
- Spearman Rank Correlation.
This segment covers the computation of the Spearman rank correlation and the Spearman rank correlation test.