isical.ac.in M.Statistics ISI Admission Sample Questions Paper : Indian Statistical Institute
Name of the University : Indian Statistical Institute
Exam : ISI Admission Test
Document Type : Sample/Previous Year Question Paper
Name of the Subject : M.Statistics
Year : 2016
Website : http://www.isical.ac.in/~admission/IsiAdmission2017/PreviousQuestion/Questions-MStat.html
Download Sample/Previous Years’ Questions :
2016 UGA(Odd) : https://www.pdfquestion.in/uploads/11325-MStatodd-2016.pdf
2016 UGA(Even) : https://www.pdfquestion.in/uploads/11325-MStateven-2016.pdf
2014 PSB : https://www.pdfquestion.in/uploads/11325-MStatPSB-2013.pdf
2013 PSB : https://www.pdfquestion.in/uploads/11325-MStatPSB-2013.pdf
2012 MS : https://www.pdfquestion.in/uploads/11325-MStatMS-2012.pdf
M.Statistics ISI Admission Sample Questions Paper :
TEST CODE : UGA
Session : Forenoon
Questions : 30
Time : 2 hours
Instruction :
** Write your Name, Registration Number, Test Centre, Test Code and the Number of this Booklet in the appropriate places on the Answer sheet.
Related : Indian Statistical Institute B.Statistics ISI Admission Test Sample Question Paper : www.pdfquestion.in/11316.html
** This test contains 30 questions in all. For each of the 30 questions, there are four suggested answers. Only one of the suggested answers is correct.
** You will have to identify the correct answer in order to get full credit for that question.
** Indicate your choice of the correct answer by darkening the appropriate oval”, completely on the answer sheet.
You will get :
** 4 marks for each correctly answered question,
** 0 marks for each incorrectly answered question and
** 1 mark for each un attempted question.
** All Rough Work Must Be Done On This Booklet Only.
** You Are Not Allowed To Use Calculator.
1. Let X and Y be independent and identically distributed random variables with moment generating function
(A) M(t)M(-t)
(B) 1
(C) (M(t))2
(D) M(t)/M(-t)
2. A 6-digit number is to be formed by rearranging the digits of 654321. How many such numbers will be divisible by 12?
(A) 168
(B) 192
(C) 360
(D) 144
3. Let A be a 2*2 matrix with real entries. If 5+3 p -1 is an eigenvalue of A, then the determinant of A equals
(A) 16
(B) 8
(C) 4
(D) 34
4. Let A and B be matrices such that B2 + AB + 2I = 0, where I denotes the identity matrix. Which of the following matrices must be non singular?
(A) B
(B) A
(C) A + 2I
(D) B + 2I
5. Let X1;X2; and X3 be independent Poisson random variables with mean 1. Then P(maxfX1;X2;X3g = 1) equals
(A) 1 – e-3
(B) e-3
(C) 1 – 8e-3
(D) 7e-3
6. Consider a confounded 25 factorial design with factors A;B;C;D;E arranged in four blocks each of size eight. If the principal block of this design consists of the treatment combinations (1); ab; de; ace, and four others, then the confounded factorial facts would be
(A) AB;DE;ABDE
(B) ABC;CDE;ABDE
(C) AB;CDE;ABCDE
(D) ABC;DE;ABCDE
7. The number of ordered pairs (a; b) such that a + b 60, where a and b are positive integers, is
(A) 1830
(B) 1770
(C) 885
(D) 3540
8. An 8-digit number is to be formed with digits from the set f1; 2; 3g such that the sum of the digits in the number is equal to 10. How many such numbers are there?
(A) 8/1+8/2
(B) 8/1
(C) 8/2
(D) 8/1*8/2
9. Let X be a random variable with probability density function where > 0. If a test of size = 0:1 for testing H0 : = 1 vs H1 : = 2 rejects H0 when X < m, then the value of m is
(A) 80/9
(B) 5
(C) 40/9
(D) 40/3
10. Let g be a differential function from the set of real numbers to itself. If g(1) = 1 and g0(x2) = x3 for all x > 0, then g(4) equals
(A) 67/5
(B) 64/5
(C) 37/5
(D) 32/5
TEST CODE: MS
Session : Afternoon
Questions: 10
Time: 2 hours
Instructions :
** Write your Name, Registration number, Test Code, Number of this booklet, etc. in the appropriate places on the answer–booklet.
** All questions carry equal weight.
** Answer at least one question from GROUP A.
** Best five answers subject to the above conditions will be considered.
** Answer to each question should start on a fresh page.
** All rough work must be done on this booklet and/or the answer–booklet.
** You are not allowed to use calculators.
GROUP A :
1. Suppose V is the space of all n×n matrices with real elements. Define T : V ! V by T (A) = AB – BA, A 2 V , where B 2 V is a fixed matrix. Show that for any B 2 V
(a) T is linear;
(b) T is not one-one;
(c) T is not onto.
GROUP B :
1. Suppose integers are formed by taking one or more digits from the following 2, 2, 3, 3, 4, 5, 5, 5, 6, 7.
For example, 355 is a possible choice while 44 is not. Find the number of distinct integers that can be formed in which
(a) the digits are non-decreasing;
(b) the digits are strictly increasing.
2. A box has an unknown number of tickets serially numbered 1, 2, . . . ,N. Two tickets are drawn using simple random sampling without replacement (SRSWOR) from the box. If X and Y are the numbers on these two tickets and Z = max(X, Y ), show that
(a) Z is not unbiased for N;
(b) aX+bY +c is unbiased for N if and only is a+b = 2 and c = -1.
3.Suppose X1,X2 and X3 are three independent and identically distributed Bernoulli random variables with parameter p, 0 < p < 1. Verify if the following statistics are sufficient for p:
(a) X1 + 2X2 + X3;
(b) 2X1 + 3X2 + 4X3.