MG221: Applied Probability & Statisticsmgmt.iisc.ac.in/CM/MG221/syl2016.pdf · MG221: Applied...

MG221: Applied Probability & StatisticsSyllabus 2016

08/08: Nature of Probabilistic Problems. Types of Statistical Studies and Types of Vari-ables. Recapitulation of Descriptive Statistics.

11/08: Samples versus the Probability Universe. Interpretation and Definition of Probabil-ity. Discrete Sample Space. Combinatiorial Probaility.

18/08: Probability Laws - Complementation, Addition and Multiplication Law. ConditionalProbability. Bayes Theorem.

22/08: Random Variables. Discrete Random Variables - p.m.f., c.d.f., Moments & Quan-tiles.

25/08: Discrete Random Variables - Chebyshev’s Inequality. Continuous Random Variables- c.d.f..

29/08: Continuous Random Variables - p.d.f., Moments, Quantiles. General Random Vari-ables.

01/09: Jointly Distributed Discrete Random Variables - Marginal & Conditional Distribu-tions. Introduction to Covariance, Correlation, & Regression.

08/09: Properties of Expectation, Variance, Covariance, Correlation, & Regression. Jointp.d.f.

15/09: Jointly Distributed Continuous Random Variables - Marginal & Conditional p.d.f.s.Probability Generating Functions.

19/09: Probability Generating Functions of Binomial, Gemoteric and Negative BinomialDistributions. Moment Generating & Characteristic Functions.

22/09: Binomial, Hypergeomtric, Geometric & Negative Binomial Distributions.

26/09: Poisson Distribution & Poisson Process.

29/09: Uniform, Exponential & Gamma Distributions.

03/10: Normal Distributions.

06/10: Introduction to R. Probability distributions in R.

13/10: Statistical Inference - Estimation, Hypothesis Testing & Forecasting. FrequentistSampling Distribution. Point Estimation Criteria - MSE, Unbiasedness, UMVUE, StandardErrors, Consistency. Law of Large Numbers.

Midterm: Saturday, October 15th, 2016 - 2:00-5:00 PM.

17/10: Point Estimation Methods - MM & MLE. Confidence Intervals.

20/10: Nature of Hypothesis Testing. Type I & Type II Errors. Size and Power of a Test.Neymann-Pearson Lemma.

24/10: Discussion of the Midterm. Fixed Significance Level Testing versus Observed Sig-nificance Level (p-value) Testing. Likelihood Ratio Test. Testing for Population Proportion.

27/10: Inference for the Mean of the Normal Distrubution. Central Limit Theorem. Infer-ence for an arbitrary Population Mean for large samples.

31/10: One Sample Problem for Normal Variance - χ2 Distribution, χ2-test, χ2-interval.One Sample Problem for Normal Mean with Unknown Variance - t distribution, t-test, t-interval.

03/11: One Sample Problem for Proportion and Population Quantiles - Binomial or Signtest. Two Independent Sample Problem for Mean for Large Samples. Two IndependentSample Problem for Proportion for Large Samples. Sample size Determination for Problemsof Mean and Proportion.

07/11: Two Independent Sample Problem for Normal Variances - F distribution, F -testand F -interval. Two Independent Sample Problem for Normal Means - Pooled & Welcht-tests.

10/11: Paired Sample Problem for Normal Means. Paired t-test. Two Independent SampleProblem for Location - Non-Parametric Wilcoxon Rank Sum Test.

17/11: One/Paired Sample Problem for Location - Non-Parametric Wilcoxon Signed RankTest. One Sample Problem for Qualitative Dependent Variable - Multinomial Distribution.

21/11: χ2 Tests for Goodness of Fit, Homegenity and Independence.

24/11: Fisher’s Exact test for the 2× 2 Contingency Tables.

Reading Material:

1. Class Notes.

2. Lecture Notes Available at http://www.mgmt.iisc.ernet.in/CM/MG221/ln.html

3. Text Books:

A. Applied Statistics and Probability for Engineers by Douglas C. Montgomery &George C. Runger. Fifth Edition, 2014. Willey.

B. Statistics by David Freedman, Robert Pisani & Roger Purves. Fourth Edition,2010. Viva Books.

C. Elementary Probability Theory with Stochastic Processes by Kai Lai Chung. ThirdEdition, 1974. Narosa Publishing House.

Grading:

IISc Norm: 50% Weightage on Sesssional & 50% Weightage on Final and then Gradingon the Curve (Relative Grading).

Sessional: Midterm Score + Assignments.

Final: Final Examination Score + Assignments.

Attendance:Will be taken and minimum 75% required (IISc stipulation).