The Mathematical Statistics (MS) of Joint Admission Test For M.Sc(JAM) test paper comprises of Mathematics (40% weightage) and Statistics (60% weightage)

Syllabus of Mathematical Statistics is

Mathematics:
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, eigenvalues 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
constant coefficients.



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. Chebyshev's inequality.

Standard Distributions: Binomial, negative binomial, geometric, Poisson,
hypergeometric, 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 exponential distributions.

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.