HOW TO PREPARE FOR IIT-JAM WITH MATHEMATICAL STATISTICS
Hello friends,I will first begin with introducing myself.I am Raghvendra Pandey,currently pursuing M.Sc in Applied Statistics & Informatics from IIT Bombay.I have completed my graduation from Ewing Christian College in session 2016.
Let me begin with opportunity in Statistics.Friends,Statistics is very good subject if you want to pursue your post graduation in Statistics.There are lot of opportunities in corporate ,teaching and research sector for Statistics students.Your chance of success will increase manyfold if you will get into premier institutes like IIT,IISC,IISER.Then an important question arise that how to prepare for IIT-JAM with Mathematical Statistics? What are the important books for preparation? Let’s begin with syllabus.
Syllabus — Mathematical Statistics (MS)
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.
IMPORTANT BOOKS(TOPIC WISE)-
Mathematics
Sequences and Series: N.N Bhattacharya’s book(I am sure ECC student are quite aware of it),Class notes(If possible Massey sir Notes) or Shanti Narayan’s Real Analysis Book
Differential Calculus: Read differential calculus book of Goarakh Prasad,Class Note(Don’t underestimate it)
Integral Calculus: Again Gorakh Prasad’s book
Matrices: Schaum series,N.N Bhattacharya’s Book,class Notes(If possible notes of S.S Tripathi Sir)
Differential Equations: Gorakh Prasad’s Book,B Rai,D.P Chaudhary’s book,class notes
Statistics
In statistics these are the topic mentioned in syllabus.I had read only class notes ,Gupta-Kapoor and V.K Rohtagi.
Probability: Introduction to probability theory, by Hoel, Port and Stone,or Gupta Kapoor,or An introduction to probability and statistics, by Rohatgi and Saleh + Class notes
Random Variables: Introduction to probability theory, by Hoel, Port and Stone,or Gupta-Kapoor,or An introduction to probability and statistics, by Rohatgi and Saleh + Class notes
Standard Distributions: Introduction to probability theory, by Hoel, Port and Stone,or Gupta-Kapoor,or An introduction to probability and statistics, by Rohatgi and Saleh + Class notes
Standard Distributions: Introduction to probability theory, by Hoel, Port and Stone,or Gupta-Kapoor,or Rohatgi and Saleh + Class notes
Sampling distributions: Introduction to probability theory, by Hoel, Port and Stone,or Gupta-Kapoor,or Rohatgi and Saleh + Class notes
Limit Theorems: Introduction to probability theory, by Hoel, Port and Stone,or Gupta-Kapoor,or An introduction to probability and statistics, by Rohatgi and Saleh + Class notes
Testing of Hypotheses- Casella berger’s Statistical inference,Gupta-Kapoor,V.K Rohtagi + Class notes
If you like you can also download the pdf of A First course in Probability, by Sheldon Ross.
Most important thing in any exam is practice with previous year papers.Believe me if you have solved 100 books but you have not practiced with previous year papers, your chance of success is limited(Exception exist).So Go to the website,download previous year papers of JAM-MS and start preparing.Don’t skip a single question of previous year paper.Previous year papers are like Brahmastra for aspirants.
IMPORTANT TOPICS-Although every topic is important ,focus more on Distribution theory,Bayes theorem ,Maximum Likelihhod Estimator,Unbiasedness,Consistency etc.
Believe me if you will follow above mentioned advice,no one can stop you from getting good JAM Rank.
Forgive me for any grammatical mistake.All the best!
Feel free to mail me at eccpandey@gmail.com.
