Indian Statistical Institute M.Tech.(QROR): MMA and PQB old question papers

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Indian Statistical Institute provides admission on the bases of the entrance test. You are asking for the Indian Statistical Institute M.Tech.(QROR): MMA and PQB old question papers.

Here I am providing you the M.Tech.(QROR): MMA and PQB old question papers and syllabus.

M.Tech.(QROR): MMA syllabus

Analytical Reasoning
Algebra | Arithmetic, geometric and harmonic progression. Continued frac-
tions. Elementary combinatorics: Permutations and combinations, Binomial theo-
rem. Theory of equations. Inequalities. Complex numbers and De Moivre's theo-
rem. Elementary set theory. Functions and relations. Elementary number theory:
Divisibility, Congruences, Primality. Algebra of matrices. Determinant, rank and
inverse of a matrix. Solutions of linear equations. Eigenvalues and eigenvectors of
matrices. Simple properties of a group.

M.Tech.(QROR): MMA sample questions


1. Let ffn(x)g be a sequence of polynomials de_ned inductively as
f1(x) = (x 􀀀 2)2

fn+1(x) = (fn(x) 􀀀 2)2; n _ 1:

Let an and bn respectively denote the constant term and the coe_cient of x
in fn(x). Then

(A) an = 4, bn = 􀀀4n
(B) an = 4, bn = 􀀀4n2

(C) an = 4(n􀀀1)!, bn = 􀀀4n
(D) an = 4(n􀀀1)!, bn = 􀀀4n2.

2. If a; b are positive real variables whose sum is a constant _, then the minimum
value of
p
(1 + 1=a)(1 + 1=b) is
(A) _ 􀀀 1=_
(B) _ + 2=_
(C) _ + 1=_
(D) none of the above.


M.Tech.(QROR): PQB syllabus

Syllabus PART I: STATISTICS / MATHEMATICS STREAM
Statistics (S1)
• Descriptive statistics for univariate, bivariate and multivariate data.
• Standard univariate probability distributions [Binomial, Poisson, Normal] and their fittings, properties of distributions. Sampling distributions.
• Theory of estimation and tests of statistical hypotheses.
• Multiple linear regression and linear statistical models, ANOVA.
• Principles of experimental designs and basic designs [CRD, RBD & LSD].
• Elements of non-parametric inference.

M.Tech.(QROR): PQB sample papers

1. Let X1 and X2 be independent χ2 variables, each with n degrees of freedom. Show that ()12122nXXXX- has the t distribution with n degrees of freedom and is independent of X1 + X2.
2. Let [{xi ; i = 1, 2, …, p}; {yj ; j = 1,2,…, q}; {zk ; k = 1, 2, …,r}] represent random samples from N(α + β, σ2), N(β + γ, σ2) and N(γ + α, σ2) populations respectively. The populations are to be treated as independent.
(a) Display the set of complete sufficient statistics for the parameters (α, β, γ, σ2).
(b) Find unbiased estimator for β based on the sample means only. Is it unique?
(c) Show that the estimator in (b) is uncorrelated with all error functions.
(d) Suggest an unbiased estimator for σ2 with maximum d.f.
(e) Suggest a test for H0: β = β0.