Semester-wise Syllabus for an MSc in Statistics

Semester 1: Foundations of Probability & Statistics

1. Probability Theory

   • Axioms, conditional probability, Bayes’ theorem

   • Random variables (discrete/continuous), distributions (Binomial, Poisson, Normal)

   • Expectation, variance, moment-generating functions

2. Mathematical Statistics

   • Sampling distributions (χ², t, F)

   • Point estimation (MLE, Method of Moments)

   • Sufficiency, completeness, Rao-Blackwell theorem

3. Linear Algebra & Calculus for Statisticians

   • Matrix operations, eigenvalues, eigenvectors

   • Multivariate calculus (optimization, Lagrange multipliers)

4. Statistical Computing (R/Python)

   • Data visualization (ggplot2, matplotlib)

   • Simulations (Monte Carlo), basic programming for stats

Semester 2: Statistical Inference & Regression

1. Statistical Inference

   • Hypothesis testing (t-tests, ANOVA, chi-square)

   • Confidence intervals, p-values, power of tests

   • Non-parametric tests (Wilcoxon, Kruskal-Wallis)

2. Regression Analysis

   • Simple & multiple linear regression

   • Model diagnostics (multicollinearity, heteroscedasticity)

   • Logistic regression (binary outcomes)

3. Design of Experiments (DoE)

   • CRD, RBD, Latin squares

   • Factorial designs, confounding

4. Stochastic Processes (Optional)

   • Markov chains, Poisson processes, Brownian motion

Semester 3: Advanced Statistics & Electives

1. Multivariate Analysis

   • Principal Component Analysis (PCA)

   • Factor analysis, cluster analysis

   • MANOVA, discriminant analysis

2. Time Series Analysis

   • ARIMA, SARIMA models

   • Forecasting, seasonality decomposition

3. Bayesian Statistics

   • Prior/posterior distributions, conjugate priors

   • MCMC (Gibbs sampling, Metropolis-Hastings)

4. Electives (Choose 1–2)

   • Machine Learning for Statisticians (Supervised/unsupervised learning)

   • Survival Analysis (Kaplan-Meier, Cox regression)

   • Spatial Statistics (Kriging, geostatistics)

   • Big Data Analytics (Hadoop, Spark basics)

Semester 4: Applied Statistics & Dissertation

1. Statistical Machine Learning

   • Decision trees, SVM, neural networks (basics)

   • Model evaluation (ROC, AUC, cross-validation)

2. Generalized Linear Models (GLMs)

   • Exponential family, link functions

   • Poisson/Negative Binomial regression

3. Dissertation/Project

   • Real-world data analysis (healthcare, finance, social sciences)

   • Research paper/report submission

4. Industry Applications (Optional)

   • Statistical consulting case studies

   • Quality control (Six Sigma, SPC)