NA387 W 07 Course Summary Review for Final Exam

1. NA387 W 07 Course SummaryReview for Final Exam Closed book, 2 (2-sided) Sheets allowed

2. What did we learn ? • Got an understanding of probabilistic aspects of the world of engineering. • Learned to analyze various types of data and problems • Most of material was foundation training, basics and fundamentals. Other courses (IOE, other Depts) cover applications and more in-depth theories.

3. My Advice is to save everything- • Especially Textbooks, lecture Notes, PPTS, formula sheets, even assignments and exams. • You will most likely need to refer to them again and again when you take higher level courses, but also in many other courses requiring Probs and Stats.

4. What we learned: • Understanding Events, Probabilities, Distributions, Density Functions. • Selecting the most appropriate distributions for analytical modeling • Selecting the best parameter estimates for Statistics • Understanding the effects of sample size and sampling errors • Following is a more detailed, Chapter by Chapter list.

5. Chapter 1: Descriptive Statistics • Understand and apply descriptive statistics (mean, standard deviation, variance, range, median) • Understand and apply basic graphical techniques (histogram, dot plot, frequency table)

6. Chapter 2: Basic Probability concepts • Understand and apply the basic concepts of Probability Theory (Events, probabilities, intersections, unions, conditional probability, independence of events, Bayes theorem, permutations and combinations)

7. Chapter 3:Discrete RVs • Discrete Random Variables, PMFs • Expected Values, Variances, • Conditional EVs and Variances! • Bernoulli and Binomial PMFs • Geometric, Hypergeometric, and negative Binomial PMFs • Poisson PMF!

8. Chapter 4:Continuous RVs • Continuous Random Variables • Probability Distributions (pdf, cdf) • Uniform Distribution • Percentiles • Expected Values and Variance • Exponential PDF and Poisson PMF!

9. N/A N/A

10. Chapter 4 (cont’d) • Normal Distribution!!! • Properties, pdf, cdf • Standardizing a variable (Must be an expert with the table!) • Percentiles, probabilities… • Transform back to original units • Normal Approximations • Binomial

11. Chapter 4 -end • Weibull Distribution • Pdf, cdf, E(X), V(X), MTTF • Exponential also a special case of Weibull • Lognormal Distribution • Pdf, cdf, E(X), V(X) • Transformation back to original units • Probability Plots • Beta Distribution • Pdf, cdf, E(X), V(X)

12. Chapter 5:Joint Distributions, Central Limit Theorem • Jointly distributed variables • Discrete • Continuous • Mixture experiments • Joint Distributions (2 independent random variables) • Expected values; Conditional Expectations • Covariance and Correlation

13. Chapter 5 (con’d) • Statistics and their distributions • Point Estimate – sampling distribution • Independent and identically distributed (iid) random samples • Deriving sampling distribution of a statistic • By probability • Simulation

14. Chapter 5 (end) • Distribution of the sample mean • Central Limit Theorem! • Distribution of a linear combination • as we stressed in the lectures, the CLT is still valid if the RVs are independent, even if they are NOT identically distributed, or with same means or variances.

15. Chapter 6: Point Estimation • Point Estimation Concepts, estimator bias and variance • MVUE (minimum variance unbiased estimator) • Standard Error • Method of Moments • Maximum likelihood Estimation (MLE)

16. Chapter 7: Confidence Intervals • Given a statistic, generate a confidence interval mean, proportion, variance Large sample CI’s for a Population Mean and Proportion CI’s based on a Normal Population CI’s for Variance and St. Dev of a Normal Population Understand effects of sample size

17. Chapter 8: Single Sample Hypothesis Testing • Understand effects of sample size and sampling error (type I and II errors) and their relative importance, on one-sample statistical decisions. • Know how to properly conduct a single sample hypothesis test • Tests about a Population Mean, Proportions. • P-values

18. Chapter 12: Simple Linear Regression and Correlation • Did only Sections 12.1 and 12.5 in detail • 12.1: The Simple Linear Regression Model • 12.5: Correlation

19. Chapter 14: Goodness-of-fit Tests • Briefly discussed the Chi-square goodness of fit test, comparing Histograms of data and “Theory” (H0) • Discussed the K-S goodness of for test, comparing cumulatives of data and ‘theory’ (not in text) • Introduced “Delphi” surveys (not in text)

20. Final Exam: The important things • To prepare for the exam, study: • 1. Lectures PPTs, and esp. examples done on the board in lectures, and in the labs • 2. Textbook chapters 1-8, Hwks 1-8. , and elements of 12 and 14 (see previous slide) • Questions will be a mix of multi choice-fill in the blanks-etc short answer problems, and full solution simple problems

21. Final Exam-Con’d • Closed book, alternate seating, two classrooms • Problems will be mostly similar to previous exams, homeworks, etc. • Prepare Well / Good Luck!

22. In Conclusion: • NA387: An important, basic course that is necessary in many future courses. • Lots of new and very useful knowledge. • Let us know (e-mail?) when you have an opportunity to use Probs and Stats in the future!