IIT JAM STATISTICS (SA) SYLLABUS

IIT JAM Statistics 2022 syllabus has been released. IIT JAM Statistics syllabus designed for IIT JAM Statistics Exam comprises 8 sections : Probability, Standard Distributions, Estimation, Random Variables, Limit Theorems, Joint Distributions, Sampling distributions, Testing of Hypotheses.

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' 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

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

Hniform

Exponential

Gamma, beta and normal distributions

Poisson and normal approximations of a binomial distribution

Limit Theorems

Weak law of large numbers

Central limit theorem (i.i.d.with finite variance case only)

Joint Distributions

Joint, marginal and conditional distributions

Distribution of functions of random variables

Joint moment generating function

Product moments, correlation, simple linear regression

Independence of random variables

Sampling distributions

Chi-square

t and F distributions, and their properties.

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.