(Syllabus) Joint Admission Test (JAM) Syllabus for Mathematical Statistics (MS) : 2009

Joint Admission Test (JAM) Syllabus for Mathematical Statistics (MS) : 2009

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's 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.

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