Transcript M50: Probability and Statistical Inference Winter 09 Instructor: Prof

Statistics text for reading:
http://www.stat.duke.edu/~michael/book.html
M50: Probability and Statistical Inference
Winter 09
Instructor: Prof. Eugene Demidenko
What is in the course? Elements of continuous probability and statistics with applications,
programming with R
What you learn? : How to solve real-life data-driven problems.
Why mathematics? You understand what you are doing in R.
No text book, electronic notes are provided by the end of the week, weekly homework.
See what I’m doing: www.dartmouth.edu/~eugened
Ask a question: [email protected]
Applications:
Statistics with images.
fMRI: how brains work.
Alcohol initiation in kids.
Text analysis:
Mark Twain or Jack
London?
Optimal portfolio
allocation
Stock price dynamics.
Genomics: microarray
distribution in cancer
patients.
Syllabus:
Part 1. Probability with R
Week 1. Cumulative distribution function and density of continuous random variable, mathematical
expectation/mean and variance, uniform and exponential distributions. Introduction to R.
Week 2. Bernoulli, binomial and Poisson distributions. Computer simulation of random variables with R,
boxplots.
Week 3. Normal distribution and Central Limit Theorem. Joint, marginal and conditional distributions.
Independence and conditional expectation, covariance, Delta method for variance calculation.
Week 4. Bivariate normal distribution, coefficient of correlation and determination, regression. Geometric
distributions on the plane, scatterplot. Optimal portfolio allocation.
Week 5. Chi-square and t-distribution, properties of the chi-square distribution.
Midterm exam on part 1.
Part 2. Statistics with R
Week 6. Statistics as an inverse problem of probability. The concept of statistical estimation and optimal
properties, unbiased and efficient estimators, mean square error.
Week 7. Method of moments, linear estimator, Gauss-Markov Theorem. Statistical simulation with R.
Week 8. Least squares estimation, correlation and regression: statistical analysis of relationship,
multivariate regression.
Week 9. Hypothesis testing, type I and type II errors, statistical significance and p-value, Z-test, unpaired
and paired t-test.
Week 10. Confidence intervals, analysis of variance (ANOVA).
Team project presentation.
Final exam on part 2.
Grades breakdown:
Homework: 30%
Midterm: 25%
Final: 30%
Team project: 15%
Examples:
Baseball, Basketball,
Car Accidents,
Height&Weight,
Life&Death