Hello aspirant,

This is the detailed syllabus(Topic wise) which you need to study for the exam-

Unit 1
Borel-contelli Lemma,Tchebycheffs and Kolmogorovs inequalities, Various modes of
convergence: in probability, almost sure, in distribution and in mean square and their inter-
relationship.
Properties of a good estimator, Concept of likelihood function, Cramer-Rao inequality,
Bhattacharya Bounds, Minimum mean square estimation, Rao-Black well theorem.

Binomial, Poisson, Geometric, Normal, Exponential, Beta and Gamma distributions. Sampling
distributions; Student-t distribution, F-distribution and Chi-square distribution. Simple tests
based on t, f, Chi-square and normal variate z.
Unit-III
Probability sampling. Sampling with equal and unequal probabilities : pps sampling with
replacement and without replacement sampling. Stratified sampling. Proportional allocation,
optimum allocation.
Basic principles of experimental design. Construction and analysis of completely randomized,
randomized blocks and Latin-square designs. Factorial experiments: symmetrical factorials.
Factorial experiment with each factor at two levels
Unit-IV
Multivariate normal distribution Marginal and Conditional distributions. Estimation of the mean
vector and covariance matrix, maximum likelihood estimator of the parameters of multivariate
normal distribution. The distribution of the sample mean vector and sample dispersion matrix.
Hottelings T2
and Mahalanobis-D2
Statistic; distribution and uses. Principal components and
Canonical correlation in the population.