# IIT JAM Mathematical Statistics Syllabus 2015

**IIT JAM 2015 Mathematical Statistics Syllabus **

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

**JAM 2015 Mathematics Syllabus**

**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.

**IIT JAM 2015 Navigation : **IIT JAM 2014 Biological Science Syllabus , IIT JAM 2015 Preparation Tips, IIT JAM 2015 Counselling, IIT JAM 2015 Syllabus , IIT JAM 2015 Results , IIT JAM 2015 Physics Syllabus, IIT JAM 2015 Mathematics Syllabus, IIT JAM 2015 Mathematical Statistics Syllabus, IIT JAM 2015 Geophysics Syllabus, IIT JAM 2015 Geology Syllabus , IIT JAM 2015 Chemistry Syllabus , IIT JAM 2015 Computer Application Syllabus , IIT JAM 2015 Biotechnology Syllabus , IIT JAM 2015 Important Dates , IIT JAM 2015 Admission Procedure , IIT JAM 2015 Exam Centres , IIT JAM 2015 Exam Pattern , IIT JAM 2015 Application Form , IIT JAM 2015 Eligibility , IIT JAM 2015 Entrance Exam , MCA Preparation Question Bank CD

**IIT JAM Related : **IIT JAM 2015 Mathematical Statistics Syllabus, IIT JAM 2015 Syllabus, IIT JAM 2015 Statistics Syllabus Detail, IIT JAM Mathematical Statistics Syllabus 2015, IIT JAM 2015 Exam Syllabus, IIT JAM 2015 MCA Syllabus, IIT JAM 2015 Syllabus Download, Syllabus for IIT JAM Mathematical Statistics 2015, IIT JAM 2015 Syllabus Material, IIT JAM 2015 Admission Test Syllabus, IIT JAM 2015 Syllabus Pattern, IIT JAM 2015 Detailed Statistics Syllabus, IIT JAM 2015 Mathematical Statistics Study Material, IIT JAM 2015 Syllabus Portion, Indian Institute of Technology Joint Admission Test Statistics Syllabus 2015, IIT JAM 2015 Syllabus Information, IIT JAM 2015 Mathematical Statistics Question Paper, IIT JAM 2015 Question Paper Download, IIT JAM 2015 Updated Syllabus, Mathematical Syllabus for IIT JAM 2015, JAM 2015 Statistical Syllabus ,

IIT JAM Statistics Syllabus 2015 – IIT JAM Syllabus for Mathematical Statistics 2015 – IIT JAM Entrance Test Syllabus 2015 – Syllabus for IIT JAM 2015 – IIT JAM Admission Syllabus 2015.

Posted In mca entrance exam : iit jam : Leave a response for **iit jam mathematical statistics syllabus 2015** by vennila