# ISI MSTAT & IITJAM Coursework This coursework is being organized by the students of ISI M.Stat batch for the preparation of the ISI MSTAT and IITJAM exams. We, the IITJAM rank holders and students from the ISI MStat batch, have united here to provide you with all the information you need to crack these examinations and get into the college of your dreams. You will find a detailed structure of the coursework below along with sample notes and materials that have been prepared by us. The classes will be held live online via Zoom and recordings of all the lectures will be available along with assignments, practice problems, a virtual library, and much more.

# Demo Notes and Problems:

#### Statistics

Note: These are just sample notes. Complete lecture notes and materials will be given to the members during the course. Please stay tuned for more updates on sample notes.

# Topics to be covered:

• Analysis: Complex Numbers, Induction, Series Sequence, Continuity, Differentiability, Integrability.
• Linear Algebra & Linear Models: Martrices (Rank,Inverses,SystemOfLinearEquations,LinearTranformations,Eigenvalues/vectors, Different Types, Decompositions,Determinants), Vector Spaces.
• Probability 1: Set, Relations, Permutations, Combinations, Elementary Counting Techniques, Multinomial Theorems, Elementary Probability, Conditional Probability, Bayes Theorem, Independence, Random Variables, PMF, PDF, CDF, Expectations, Moments, MGF, Standard Distributions, Distribution of Function of RV, Distribution of Order Statistics.
• Probability 2: Joint Probability Distribution, Marginal, and Conditional Probability Distribution, Convergence Relations, Multivariate Distributions, WLLN, SLLN, Applications.
• Statistics 1:
Part (a): Basics of Statistics (16 classes)
Introduction: Purpose of statistics. Population vs Sample. Parameter vs Statistics.
Random Variables, PMF, PDF, CDF, Expectations, Moments, MGF, Discrete & Continuous Distributions, Standard Distributions (comprehensive) with real examples.
Descriptive statistics: mean-median-mode-sd-skewness-kurtosis. Sampling distribution (chi-square, t and F and their properties), CLT.
Estimation: Estimator vs Estimate, Good properties of Estimators: Unbiasedness, minimum variance, sufficiency. Method of Estimation: Moments, MLE, examples & problems. Method for evaluating estimator: MSE, Sufficiency. Factorization theorem, Completeness, Rao-Blackwell, Cramer-Rao, UMVUE.
Confidence Interval, Normal and Exponential example.
Part (b): Design of Experiments and Sample Survey (8 classes)
Conventional sampling techniques: SRSWR, SRSWOR, Stratified sampling.
Basics of ANOVA model. Experimental designs: CRD, RBD, LSD.
• Statistics 2: (12 classes)
Hypothesis Testing: Basic Concepts: type1-2 error, power function, p-values. NP lemma & applications. LRT. Examples and problems.
Correlation & Regression: Joint, marginal & cond. distributions. Product Moments Correlation & Spearman Rank correlation. Simple Linear Regression and Multiple linear regression. Inference related to regression. Independent random variable and its relationship with correlation-regression. Interlink between Correlation & Regression.

#### The whole course will consist of 150 lectures, a total of 300 hours of live lectures along with Mock Tests.

A detailed description of the course and sample problems are below.

# Course Plan

#### Analysis #### Probability Theory #### Statistics #### High School Syllabus 