# JAM Mathematical Statistics Entrance Test Syllabus 2015

JAM 2015 Mathematical Statistics (MS) Test Syllabus/Cut Off Marks/Total Seats

The Mathematical Statistics (MS) test paper comprises of mathematics (40% weightage) and statistics (60% weightage).

Mathematics

Sequences and Series: Convergence of sequence of real number,comparison, root and ratio test of convergence of sequence of real numbers.
Differential Calculus: limits, continuity and differentiability of function of one and two variable. Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of function one and two variables.

Integral calculus: Fundamental theorem of integral calculus. Dobule and tripal intergrals application of definite integrals, arc lengths areas and volumes.
Matrices: Rank, inverse of a matrix. system of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem symmetric and skew-  symmetric and orthogonal matrices.

Differential equations: Ordinary differential equations of the first order of the form y' = f(x,y). linear differential equation 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 function, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function. Chebyshev's inequality.

Standard Distribution: Binomial, negative binomial geometric, Poisson,  hypergeometric,  unjform, exponential, gamma, beta and normal distributions. Poisson and normal approximation of a binomial distribution.

Joint Distribution: Joint marginal and conditional distribution. Distribution of functional 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 Theorem: Weak law of large numbers. Central limit theorem(i.i.d. with finite variance case only).

Estimation: Unbiasedness, consistency and efficiency of estimator, methods of moment & method of maximum livelihood, Sufficiency, factorization theorem, completeness, Rao-Blackwell& Lehmann Scheffe theorem, uniform minimum variance unbiased estimator, Rao Cramer Inequality, Confidence intervals for parameter of unvariate normal & one parameter exponential distribution.

Testing of Hypothesis - Basic concepts, application of Neyman-Pearson Lemma for testing simple & composite hypothesis, Likelihood ratio tests for parameter of unvariate normal distribution.