__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__*Convergence of sequence of real number,comparison, root and ratio test of convergence of sequence of real numbers.*

**Sequences and Series:****: 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.**

__Differential Calculus__**: Fundamental theorem of integral calculus. Dobule and tripal intergrals application of definite integrals, arc lengths areas and volumes.**

__Integral calculus__**Rank, inverse of a matrix. system of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem symmetric and skew- symmetric and orthogonal matrices.**

__Matrices:__**: Ordinary differential equations of the first order of the form y' = f(x,y). linear differential equation of the second order with constant coefficients.**

__Differential equations__

__Statistics____: Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes theorem and independence of events.__

*Probability***: 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.**

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

__Standard Distribution__**: Joint marginal and conditional distribution. Distribution of functional of random variables. Product moments, correlation, simple linear regression. independence of random variables.**

__Joint Distribution__**: Chi-square, t and F distributions, and their properties.**

__Sampling Distributions__**Weak law of large numbers. Central limit theorem(i.i.d. with finite variance case only).**

__Limit Theorem:__**: 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.**

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

__Testing of Hypothesis__
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