JAM Mathematical Statistics Entrance Test Syllabus 2015

<div dir="ltr" style="text-align: left;" trbidi="on"> <span style="font-size: large;"><b><u>JAM 2015 Mathematical Statistics (MS) Test Syllabus/Cut Off Marks/Total Seats</u></b></span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;">The Mathematical Statistics (MS) test paper comprises of mathematics (40% weightage) and statistics (60% weightage).</span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><b><u>Mathematics</u></b></span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><i><u><b>Sequences and Series:</b></u></i> Convergence of sequence of real number,comparison, root and ratio test of convergence of sequence of real numbers.</span><br /> <div class="separator" style="clear: both; text-align: center;"> </div> <span style="font-size: large;"><b><i><u>Differential Calculus</u></i></b>: 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.</span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><b><i><u>Integral calculus</u></i></b>: Fundamental theorem of integral calculus. Dobule and tripal intergrals application of definite integrals, arc lengths areas and volumes.</span><br /> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDXV0vs8P7vY9aJca_su8vBQzgHvcUB2OjjHjujJJgYCYO2UM-w4Xj1Hygus9QJR9cgDTQL4xoDs9LDFz08fYQS5XMErGTzLDTsFKJq1yTaH9qQP1g-ylGuE-4bkcCenyBDQ905T4s2QA/s1600/jam+2015.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="JAM 2015 Test Syllabus" border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDXV0vs8P7vY9aJca_su8vBQzgHvcUB2OjjHjujJJgYCYO2UM-w4Xj1Hygus9QJR9cgDTQL4xoDs9LDFz08fYQS5XMErGTzLDTsFKJq1yTaH9qQP1g-ylGuE-4bkcCenyBDQ905T4s2QA/s1600/jam+2015.jpg" title="JAM 2015 Test Syllabus" width="194" /></a></div> <span style="font-size: large;"><b><i><u>Matrices:</u></i></b> Rank, inverse of a matrix. system of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem symmetric and skew-  symmetric and orthogonal matrices.</span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><b><i><u>Differential equations</u></i></b>: Ordinary differential equations of the first order of the form y' = f(x,y). linear differential equation of the second order with constant coefficients.</span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><b><u>Statistics</u></b></span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><u><b><i>Probability</i></b></u>: Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes theorem and independence of events.</span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><b><i><u>Random Variables</u></i></b>: 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.</span><br /> <span style="font-size: large;"><br /></span> <span style="font-size: large;"><b><i><u>Standard Distribution</u></i></b>: Binomial, negative binomial geometric, Poisson,  hypergeometric,  unjform, exponential, gamma, beta and normal distributions. Poisson and normal approximation of a binomial distribution.</span><br /> <span style="font-size: large;"><br /></span> <div style="text-align: left;"> <span style="font-size: large;"><b><i><u>Joint Distribution</u></i></b>: Joint marginal and conditional distribution. Distribution of functional of random variables. Product moments, correlation, simple linear regression. independence of random variables.</span></div> <div style="text-align: left;"> <span style="font-size: large;"><br /></span></div> <div style="text-align: left;"> <span style="font-size: large;"><b><i><u>Sampling Distributions</u></i></b>: Chi-square, t and F distributions, and their properties.</span></div> <div style="text-align: left;"> <span style="font-size: large;"><br /></span></div> <div style="text-align: left;"> <span style="font-size: large;"><b><i><u>Limit Theorem:</u></i></b> Weak law of large numbers. Central limit theorem(i.i.d. with finite variance case only).</span></div> <div style="text-align: left;"> <span style="font-size: large;"><br /></span></div> <div style="text-align: left;"> <span style="font-size: large;"><b><i><u>Estimation</u></i></b>: 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.</span></div> <div style="text-align: left;"> <span style="font-size: large;"><br /></span></div> <div style="text-align: left;"> <span style="font-size: large;"><b><i><u>Testing of Hypothesis</u></i></b> - Basic concepts, application of Neyman-Pearson Lemma for testing simple & composite hypothesis, Likelihood ratio tests for parameter of unvariate normal distribution.</span></div> </div>

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 ma...

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