MG221: Applied Probability & Statistics
Syllabus 2018
06/08: Nature of Probabilistic and Statistical Problems. Types of Statistical Studies and
Types of Variables. Recapitulation of Descriptive Statistics.
09/08: Samples versus the Probability Universe. Interpretation and Definition of Probabil-
ity. Discrete Sample Space. Combinatiorial Probability.
13/08: Probability Laws - Complementation, Addition and Multiplication Law. Conditional
Probability. Bayes Theorem.
16/08: Random Variables. Discrete Random Variables - p.m.f., c.d.f., Moments & Quan-
tiles.
20/08: Discrete Random Variables - Chebyshev’s Inequality. Continuous Random Variables
- c.d.f..
23/08: Continuous Random Variables - p.d.f., Moments, Quantiles. General Random Vari-
ables.
27/08: Jointly Distributed Discrete Random Variables - Marginal & Conditional Distribu-
tions.
30/08: Introduction to Covariance, Correlation, & Regression. Properties of Expectation,
Variance, Covariance, Correlation, & Regression.
03/09: Jointly Distributed Continuous Random Variables - Joint, Marginal & Conditional
p.d.f.s. Probability Generating Functions.
06/09: Probability Generating Functions of Binomial, Geometric and Negative Binomial
Distributions. Moment Generating & Characteristic Functions.
10/09: Binomial, Hypergeometric, Geometric & Negative Binomial Distributions.
17/09: Poisson Distribution & Poisson Process.
20/09: Uniform, Exponential & Gamma Distributions.
24/09: Normal Distributions.
27/09: Introduction to R. Probability distributions in R.
Midterm: Saturday, September 29th , 2018 - 2:00-5:00 PM.
01/10: Statistical Inference - Estimation, Hypothesis Testing & Forecasting. Frequentist
Sampling Distribution.
04/10: Point Estimation Criteria - MSE, Unbiasedness, UMVUE, Standard Errors, Consis-
tency. Convergence of Random Variables. Law of Large Numbers. Central Limit Theorem.
11/10: Point Estimation Methods - Method of Moments & Method of Maximum Likelihood.
Confidence Intervals.
15/10: Discussion of the Midterm. Nature of Hypothesis Testing.
18/10: Type I & Type II Errors in Hypothesis Testing. Size and Power of a Test. Neymann-
Pearson Lemma. Testing for the Mean of a Normal Distribution with known Variance.
22/10: Fixed Significance Level Testing versus Observed Significance Level (p-value) Test-
ing. Likelihood Ratio Test. Inference for a Population Proportion. Inference for a Population
Mean for large samples.
25/10: 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.
29/10: Two Independent Sample Problem for Mean and Proportion for Large Samples.
Sample size Determination for Problems of Mean and Proportion.
05/11: Two Independent Sample Problem for Normal Variances - F distribution, F -test
and F -interval. Two Independent Sample Problem for Normal Means - Pooled & Welch
t-tests.
08/11: Paired Sample Problem for Normal Means. Paired t-test. Introduction to Non-
Parametrics. Empirical CDF. ECDF based and other tests for Normality.
12/11: Two Independent Sample Problem for Location - Wilcoxon Rank Sum Test. One/Paired
Sample Problem for Location - Binomial or Sign test, Extended to tests for Population Quan-
tiles.
15/11: One/Paired Sample Problem for Location - Wilcoxon Signed Rank Test. One Sam-
ple Problem for Qualitative Dependent Variable - Multinomial Distribution. χ2 Test for
Goodness of Fit for discrete models.
19/11: χ2 Tests for Homogeneity and Independence. Fisher’s Exact test for the 2 × 2
Contingency Tables.
22/11: Implementation of the learnt methods in R.
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. Third
Edition, 1974. Narosa Publishing House.
Grading:
IISc Norm: 50% Weightage on Sessional & 50% Weightage on Final and then Grading
on the Curve (Relative Grading).
Sessional: Midterm Score + Assignment.
Final: Final Examination Score + Assignment.
Attendance:
Will be taken and minimum 75% required (IISc stipulation).
