Statistics

In order to get admission for M.Sc programs in IITs & IISc, The Joint Admission Test(JAM) for M.Sc is being conducted to provide admissions to M.Sc. (4 Semesters), Joint M.Sc-Ph.D, M.Sc-Ph.D, Dual Degree, etc.
Eligibility Criteria: Candidates to hold a Bachelor's Degree. Candidates belonging to General/OBC (Non-Creamy Layer) category must have at least 55% aggregate in Bachelors. Further, students those are in final year of graduation can also apply for JAM. You are eligible for the following programs as under:
1. Joint M.Sc-Ph.D in Mathematics
2. MSc-Ph.D dual degree in Operation research
3. M.Sc applied statistic and informatics and 4.
4. M.Sc Statistics
The JAM syllabus of Mathematical statistic is as under:
1. Mathematics (a) Sequences and Series: Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.
(b) 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.
(c) Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.
(d) Matrices: Rank, inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices.
2. Statistics :- (a) Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes theorem and independence of events.
(b) 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.
(c) Standard Distributions: Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution. (d) 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. (e) Sampling distributions: Chi-square, t and F distributions, and their properties.