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This course provides a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. The topics include hypothesis testing and estimation. It also includes confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. In addition to that, estimates by method of moments, their properties, maximum likelihood estimates, their properties, Fisher information, Rao-Cramer inequality and efficient estimates Bayes estimates.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
| Module: 01 | |||
| Introduction | 00:45:00 | ||
| Some Probability Distributions | 00:10:00 | ||
| Method of Moments | 00:10:00 | ||
| Maximum Likelihood Estimators | 00:10:00 | ||
| Consistency of MLE | 00:10:00 | ||
| Rao-Crámer Inequality | 00:10:00 | ||
| Efficient Estimators | 00:10:00 | ||
| Gamma Distribution | 00:10:00 | ||
| Prior and Posterior Distributions | 00:10:00 | ||
| Bayes Estimators | 00:10:00 | ||
| Sufficient Statistic | 00:10:00 | ||
| Module: 02 | |||
| Jointly Sufficient Statistics | 00:10:00 | ||
| Minimal Jointly Sufficient Statistics | 00:10:00 | ||
| Estimates of Parameters of Normal Distribution | 00:10:00 | ||
| Orthogonal Transformation of Standard Normal Sample | 00:10:00 | ||
| Fisher and Student Distributions | 00:10:00 | ||
| Confidence Intervals for Parameters of Normal Distribution | 00:10:00 | ||
| Testing Hypotheses | 00:10:00 | ||
| Most Powerful Test for Two Simple Hypotheses | 00:10:00 | ||
| Randomized Most Powerful Test | 00:10:00 | ||
| Monotone Likelihood Ratio | 00:10:00 | ||
| One Sided Hypotheses (cont.) | 00:10:00 | ||
| Module: 03 | |||
| Pearson’s Theorem | 00:10:00 | ||
| Goodness-of-Fit Test | 00:10:00 | ||
| Goodness-of-Fit Test for Composite Hypotheses | 00:10:00 | ||
| Test of Independence | 00:10:00 | ||
| Test of Homogeneity | 00:10:00 | ||
| Kolmogorov-Smirnov Test | 00:10:00 | ||
| Simple Linear Regression | 00:10:00 | ||
| Joint Distribution of the Estimates | 00:10:00 | ||
| Statistical Inference in Simple Linear Regression | 00:10:00 | ||
| Classification Problem | 00:10:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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