# JAM 2012 Exam Syllabus - MS (Mathematical Statistics)

## Syllabus: Joint Admission Test For M.Sc. 2012

## Mathematical Statistics (MS)

The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weight age) and Statistics (60% weight age).

## 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, 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
constant coefficients.

**Statistics Probability:** Axiomatic definition of probability and properties,
conditional probability, multiplication rule. Theorem of total probability.
Bayesâ€™ 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,
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
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.

Courtesy: iitb.ac.in