IIT JAM 2016 Examination : Mathematical Statistics (MS) Syllabus

IIT Joint Admission Test-2016 Examination Syllabus

JAM Mathematical Statistics (MS) 2016 Syllabus

Indian Institute Of Technology Conducts The JAM-2016 (Joint Admission Test-2016) For Admission in M.Sc. Courses in IIT's. In 2016 IIT Madras Conducts The Exam For Seven Various Subjects Program For M.Sc. Admission. JAM-2016 Mathematical Statistics (MS) Syllabus is given Below :

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

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, 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-2016 Syllabus : Biological Sciences (BL) | Biotechnology (BT) I Chemistry (CY) | Geology (GG) | Mathematics (MA) | Mathematical Statistics (MS) | Physics (PH) I