Core papers for the three-year B.Sc. Statistics programme under Tamil Nadu state university CBCS regulations.

BSC-STAT-DOE — Design of Experiments (B.Sc. Statistics)

Design of Experiments (B.Sc. Statistics)

Analysis of variance and standard experimental designs including CRD, RBD, LSD and factorial experiments.

📋 Course Learning Outcomes

On successful completion of this course, the learner will be able to:

  1. Apply one-way and two-way analysis of variance to test equality of treatment means [Apply]
  2. Explain the principles of randomisation, replication and local control in experimental design [Understand]
  3. Analyse data from completely randomised, randomised block and Latin square designs [Analyze]
  4. Apply the missing plot technique and analysis of covariance to handle incomplete or covariate-adjusted data [Apply]
  5. Construct and interpret 2^2 and 2^3 factorial experiments including total and partial confounding [Create]
  6. Evaluate the relative efficiency of competing experimental designs for a given research question [Evaluate]

📚 Chapters

  1. Unit I — Analysis of variance: one-way and two-way classification
  2. Unit II — Principles of design of experiments and CRD
  3. Unit III — Randomised block design and Latin square design
  4. Unit IV — Missing plot technique and analysis of covariance
  5. Unit V — Factorial experiments: 2^2, 2^3 and confounding

TutorDA LMS

BSC-STAT-SAMP — Sampling Theory (B.Sc. Statistics)

Sampling Theory (B.Sc. Statistics)

Theory and methods of sample surveys including SRS, stratified, systematic and cluster sampling.

📋 Course Learning Outcomes

On successful completion of this course, the learner will be able to:

  1. Distinguish between sampling and non-sampling errors and identify their sources in survey design [Understand]
  2. Apply simple random sampling with and without replacement to estimate population means and totals [Apply]
  3. Compare proportional, optimum and Neyman allocation methods in stratified random sampling [Analyze]
  4. Evaluate ratio and regression estimators in systematic sampling for efficiency gains over SRS [Evaluate]
  5. Design cluster, two-stage and PPS sampling schemes for large-scale official surveys [Create]
  6. Compute standard errors and relative efficiencies of competing sampling estimators [Apply]

📚 Chapters

  1. Unit I — Concepts of population, sample, sampling and non-sampling errors
  2. Unit II — Simple random sampling with and without replacement
  3. Unit III — Stratified random sampling and allocation methods
  4. Unit IV — Systematic sampling and ratio and regression estimators
  5. Unit V — Cluster sampling, two-stage sampling and PPS sampling

TutorDA LMS

BSC-STAT-INF — Statistical Inference (B.Sc. Statistics)

Statistical Inference (B.Sc. Statistics)

Estimation theory, properties of estimators and tests of hypotheses including parametric and non-parametric tests.

📋 Course Learning Outcomes

On successful completion of this course, the learner will be able to:

  1. Evaluate point estimators for unbiasedness, consistency, efficiency and sufficiency [Evaluate]
  2. Derive maximum likelihood and method of moments estimators for standard parametric families [Apply]
  3. Construct confidence intervals for population mean, variance and proportion under normality assumptions [Create]
  4. Apply the Neyman-Pearson lemma to obtain most powerful tests for simple hypotheses [Apply]
  5. Conduct chi-square, t and F tests and interpret their outcomes in applied settings [Apply]
  6. Compare parametric and non-parametric tests such as the sign test and Mann-Whitney U test for given data [Analyze]

📚 Chapters

  1. Unit I — Point estimation, unbiasedness, consistency and efficiency
  2. Unit II — Methods of estimation: MLE, method of moments and minimum variance
  3. Unit III — Interval estimation and confidence intervals
  4. Unit IV — Testing of hypotheses, Neyman-Pearson lemma and likelihood ratio tests
  5. Unit V — Chi-square, t, F tests and non-parametric tests

TutorDA LMS

BSC-STAT-PROB — Probability Theory (B.Sc. Statistics)

Probability Theory (B.Sc. Statistics)

Axiomatic probability, random variables, distributions, expectation and limit theorems.

📋 Course Learning Outcomes

On successful completion of this course, the learner will be able to:

  1. Apply the axiomatic definition of probability and Bayes' theorem to compute conditional probabilities [Apply]
  2. Define discrete and continuous random variables and derive their distribution and density functions [Understand]
  3. Compute means, variances and moments for binomial, Poisson and geometric distributions [Apply]
  4. Analyze properties of normal, exponential, gamma and beta distributions and their interrelationships [Analyze]
  5. Apply moment generating and characteristic functions to derive distributions of sums of independent random variables [Apply]
  6. Use Chebyshev's inequality and the weak law of large numbers to bound probabilities and assess convergence [Evaluate]

📚 Chapters

  1. Unit I — Axiomatic probability, conditional probability and Bayes' theorem
  2. Unit II — Random variables, distribution functions and expectation
  3. Unit III — Standard discrete distributions: binomial, Poisson, geometric
  4. Unit IV — Standard continuous distributions: normal, exponential, gamma, beta
  5. Unit V — Generating functions, Chebyshev inequality and limit theorems

TutorDA LMS