LBS Centre for Science & Technology State Eligibility Test Statistics Question Paper 2017

Name of the Organisation : LBS Centre for Science & Technology
Exam : State Eligibility Test
Subject : Statistics
Year : 2017 Feb
Document Type : Model & Past Question Papers

Website : https://lbscentre.in/
Statistics 2010 : https://www.pdfquestion.in/uploads/13449-Stat2010.pdf
Statistics 2012 : https://www.pdfquestion.in/uploads/13449-Stat2012.pdf
Statistics 2013-Jun : https://www.pdfquestion.in/uploads/13449-Stat2013Jun.pdf
Statistics 2013-Dec : https://www.pdfquestion.in/uploads/13449-Stat2015Dec.pdf
Statistics 2015-Jun : https://www.pdfquestion.in/uploads/13449-Stst2015Jun.pdf
Statistics 2015-Dec : https://www.pdfquestion.in/uploads/13449-Stat2015Dec.pdf
Statistics 2016-Jun : https://www.pdfquestion.in/uploads/13449-Stat2016.pdf

State Eligibility Test Statistics Question Paper :

Time : 120 Minutes

Related : LBS Centre for Science & Technology State Eligibility Test Sociology Question Paper 2017 : www.pdfquestion.in/13446.html

1. Which of the following properties of R is known as Archimedes property?
A) Every non-empty set of reals which is bounded above has the least upper bound.
B) For any real x, there exists a unique integer m such that m x < m + 1.
C) If x 2 R, then there exists a natural number n (depending on x) such that x < n.
D) Between any two distinct real numbers, there are infinitely many rational numbers.

2. Given that N is the set of natural numbers, Q is the set of rationals, Z is the set of all integers and [0; 1] is the set of reals between 0 and 1. Then state which of the above sets is a compact set?
A) N
B) Q
C) Z
D) [0, 1]

Regarding continuity and differential of a real valued function f, consider the following statements
1. If f is continuous at a point a, then it is not necessary that f is differential at a.
2. If f is not continuous at a, then it cannot be differential at a.
Which of these statements is/are true?
A) 1 only
B) 2 only
C) Both 1 and 2
D) None of these

4. Given S1 = f(1; 0; 2); (0; 1; 2); (4;-2; 4)g and S2 = f(1; 2; 3); (0:5; 1; 1:5); (1:5; 3; 4:5)g two sets of vectors from R3. Then which of the following is correct?
A) Both S1 and S2 are linearly independent set of vectors
B) Both S1 and S2 are linearly dependent set of vectors
C) Vectors in S1 are linearly independent but those in S2 are not
D) Vectors in S2 are linearly independent but those in S1 are not

5. If A and B are symmetric matrices of the same order, then which one of the following is not correct?
A) A + B is a symmetric matrix
B) AB + BA is a symmetric matrix
C) AB is a symmetric matrix
D) A + AT and B + BT are symmetric matrices

6. The Lebesgue outer measure of an interval is its
A) initial point
B) midpoint
C) Final point
D) length

7. If A and B are independent events with P(A) = 0:3 and P(B) = 0:4, then probability that A does not occur but B occurs is
A) 0.70
B) 0.28
C) 0.21
D) 0.18

8. If an event A is independent of itself, then the value of P(A) is
A) 0
B) 1/2
C) 1
D) 0 or 1

9. Chebychev’s inequality is a special case of the inequality
A) Liapunouv
B) Kolmogorov
C) Jensen
D) Markov

10. The characteristic function of a random variable which is degenerate at 0 is
A) e-t
B) eit
C) et
D) 1

11. Which of the following is not correct on the real line?
A) The set of all integral points on R has no limit points at all
B) The set of all integral points on R is not closed
C) The empty set Ø is open while R is closed
D) Every Cauchy sequence in R converges to a limit in R

12. Consider the following sets: S1 is the set of all 2 x 2 non-singular matrices of real numbers and S2 is the set of all 2 x 2 singular matrices of real numbers. Then which of the following is correct?
A) Both S1 and S2 are vector spaces
B) Neither S1 nor S2 are vector spaces
C) S1 is a vector space whereas S2 is not
D) S2 is a vector space whereas S1 is not

13. Suppose A and B are events with probabilities defined by P(A) = p, P(B) = 1 – 2p and P(AUB) = 0.68 where 0< p < 1. Then for what value of p, the events A and B are independent?
A) 0.4
B) 0.3
C) 0.2
D) 0.5

14. There are two identical urns. First urn contains 3 black and 2 white balls whereas the second urn contains 2 black and 3 white balls. One of the urn is selected and a ball drawn at random. It was observed as a white ball. Then what is the probability that it was drawn from the second urn?
A) 2/5
B) 1/5
C) 3/5
D) 3/10

15. Given a random sample of five observations from a distribution with cdf F(x). If so, identify the statistic for which the distribution function is 5[F(x)]4 – 4 [F(x)]5, from among the following?
A) First order statistic
B) Median of the sample
C) Largest order statistic
D) Fourth order statistic