STAT 341

Topics to be covered

• Basic use of R and RStudio, maybe Posit Cloud
• Simulating coins and dice
• Simulating random variables
• Understand and interpret theoritical results empirically

Sample Survey for ISI M.Stat Entrance

Topics to be covered:

• Simple Random Sampling
• Stratified Random Sampling
• Cluster and Two Stage Sampling
• Sample Survey from a Probabilistic Viewpoint
• Problem Solving

Linear Models for ISI M.Stat Entrance

Topics to be covered:

• Theory of Linear Models
• One way and two way ANOVA
• Fixed effexts and random effects models
• A glimpse into Design of Experiments : CRD and RBD
• Problem Solving

Introduction to Probability Theory

Topics to be covered:

• Classical Definition of Probability, Algebra of Events
• Axiomatic Definition of Probability, Glimpse of Measure theory
• Conditional Probability and Independence
• Random Variables and Probability Distributions
• Probabilistic Inequalities
• Generating Functions
• Bivariate and Multivariate Distributions
• Standard Discrete, Standard Continuous Distributions
• Multivariate Normal and Multinomial Distribution
• Sampling Distributions
• Convergence Methods in Probability, Law of Large Numbers, Central Limit Theorem
• Problem Solving

Statistical Inference

Topics to be covered:

• Idea of Point Estimation
• Unbiasedness and Minimum Variance
• BLUE, UMVUE, CRLB
• Sufficiency and Completeness
• Neyman Fisher, Rao Blackwell and Lehmann Scheffe Theorem
• Method of Moments and Maximum Likelihood Estimation
• Idea of Testing of Hypothesis, Null and Alternate Hypotheses
• Size, level, Power, Errors in testing, Simple and Composite Hypotheses
• Neyman Pearson Lemma, MP and UMP tests
• Likelihood Ratio Test
• Problem Solving