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Old 8th December 2012, 12:03 PM
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Default IIT JAM Statistics Entrance

I applied for the IIT JAM and I am going to take part in the IIT JAM entrance but I need the syllabus for Mathematical Statistics so will you please provide.
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Old 10th December 2012, 10:48 AM
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Join Date: May 2012
Default Re: IIT JAM Statistics Entrance

Here I am providing the syllabus of Mathematical Statistics for IIT JAM entrance exam.

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

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.

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

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.

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.
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