Syllabus: Joint Admission Test For
Mathematical Statistics (MS)
The Mathematical Statistics (MS) test paper comprises of Mathematics (40%
weight age) and Statistics (60% weight age).
Sequences and Series: Convergence of sequences of real numbers, Comparison, root
and ratio tests for convergence of series of real numbers.
Differential Calculus: Limits, continuity and differentiability of functions of
one and two variables. Rolle's theorem, mean value theorems, Taylor's theorem,
indeterminate forms, maxima and minima of functions of one and two variables.
Integral Calculus: Fundamental theorems of integral calculus. Double and triple
integrals, applications of definite integrals, arc lengths, areas and volumes.
Matrices: Rank, inverse of a matrix. systems of linear equations. Linear
transformations, Eigen values and eigenvectors. Cayley-Hamilton theorem,
symmetric, skew-symmetric and orthogonal matrices.
Differential Equations: Ordinary differential equations of the first order of
the form y' = f(x,y). Linear differential equations of the second order with
Statistics Probability: Axiomatic definition of probability and properties,
conditional probability, multiplication rule. Theorem of total probability.
Bayes’ theorem and independence of events.
Random Variables: Probability mass function, probability density function and
cumulative distribution functions, distribution of a function of a random
variable. Mathematical expectation, moments and moment generating function.
Standard Distributions: Binomial, negative binomial, geometric, Poisson,
hyper geometric, uniform, exponential, gamma, beta and normal distributions.
Poisson and normal approximations of a binomial distribution.
Joint Distributions: Joint, marginal and conditional distributions. Distribution
of functions of random variables. Product moments, correlation, simple linear
regression. Independence of random variables.
Sampling distributions: Chi-square, t and F distributions, and their properties.
Limit Theorems: Weak law of large numbers. Central limit theorem (i.i.d.with
finite variance case only).
Estimation: Unbiasedness, consistency and efficiency of estimators, method of
moments and method of maximum likelihood. Sufficiency, factorization theorem.
Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum
variance unbiased estimators. Rao-Cramer inequality. Confidence intervals for
the parameters of univariate normal, two independent normal, and one parameter
Testing of Hypotheses: Basic concepts, applications of Neyman-Pearson Lemma for
testing simple and composite hypotheses. Likelihood ratio tests for parameters
of univariate normal distribution.