gpsc.gujarat.gov.in Administrative Service Main Exam Statistics Sample Paper : Public Commission

Organisation : Gujarat Public Service Commission
Post : Main Exam, Gujarat Administrative Service Class-1 & Class-2
Document Type : Sample Paper
Subject : Statistics
Website : https://gpsc.gujarat.gov.in/Archieved/sample-papers.html
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/25543-Statistics.pdf

GPSC Main Exam Statistics Sample Paper

Time : 100 Minutes
Total Ques. : 200
Total Marks : 200

Related : GPSC Gujarat Administrative Service Main Exam General Studies Sample Paper : www.pdfquestion.in/25537.html

Subject Code : QDB-37
Main Examination : Statistics
English Medium :
Time : 3 Hours

Instructions

(1) The question paper has been divided into three parts, A, B and C. The number of questions to be attempted and their marks are indicated in each part.

(2) Answers of all the questions of each part should be written continuously in the answer sheet and should not be mixed with other parts’ Answer. In the event of answer found, which are belongs to other part, such answers will not be assessed by examiner.

(3) The candidate should write the answer within the limit of words prescribed in the parts A, B and C.
(4) If there is any difference in English language question and its Gujarati Translation, then English language question will be considered as valid.

(5) Answer should be written in one of the two languages. Write in the language (English or Gujarati) preference given by you. Answer should not be written in both the languages in the same paper.

Sample Question

Instructions : (1) Question No. 1 to 20.
(2) Attempt all 20 questions.
(3) Each question carries 2 marks.
(4) Answer should be given approximately in 20 to 30 words.

Part-A

1. A continuous random variable X has a probability density function f(x) = 3×2, 0 < x < 1. Find ‘a’ such that p(x < a) = p(x > a).

2. For a binomial random variable x, find the value of p, if n = 6 and 9p(x = 4) = p(x = 2).
3. Mention some of the important properties of Normal distribution.
4. Given r = 0.8, nS i=1 (x – –x) (y – –y) = 60, sy = 2.5 and nS i=1 (x – –x)2 = 90. Obtain the value of n.

5. Define process control.
6. What is the significance of Average Sample number ?
7. If x is uniformly distributed in (–1, 1) and if y = x2, then what is the covariance between x and y ?

10. Write Weddle’s formula for numerical integration.
11. State the invariance property of Maximum Likelihood Estimator (MLE).
12. What is the advantages of factorial experiments ?
13. Distinguish between sign test and Wilcoxon’s signed rank test.

14. Distinguish between complete confounding and partial confounding.
15. Define consumer’s risk.
16. Convert 0.625 to its equivalent binary number.
17. If the observation recorded on five sampled items are 3, 4, 4, 8, 12, what will be the value of sample variance ?

18. A manufacturer who produces medicine bottles, finds that 0.1% of the bottles aredefective. The bottles are packed in boxes containing 500 bottles. A drug manufacturer buys 100 boxes from the producer. Using Poisson approximation, find how many boxes will contains no defective bottles. (Given e–0.5 = 0.6065).

19. State all important properties of BIBD.
20. What are non-impact printers ? Give five categories of non-impact printers.

Part-B

Instructions : (1) Question No. 21 to 32.
(2) Attempt all 12 questions.
(3) Each question carries 5 marks.
(4) Answer should be given approximately in 50 to 60 words.

21. Why do we require axiomatic definition of probability ? Give an example, where this is applicable.
22. For a two dimensional continuous random variate (x, y) with joint probability density function given by
23. Define Negative binomial distribution. Mention its chief characteristics. Give examples from real life situations where it is applicable.

25. Explain single sampling plan. Mention its limitations.
26. Write any four properties of Cobb-Douglas production function.
28. Let T0 be an MVUE, while T1 is an unbiased estimator with efficiency e?, then show that no unbiased linear combination of T0 and T1 can be MVUE.

29. Two samples from two normal populations having equal variances of size 10 and 12 have mean 12 and 10 and variances 2 and 5 respectively. Obtain 90% confidence limits for the difference between two population means. (Given t0.05, 20 = 2.086)

30. Evaluate loge7 by Simpson’s 13 rd rule and compare its value.
31. Differentiate between IF statement and SWITCH statement.
32. Define price elasticity of demand. Interpret the term elasticity.

Part-C

Instructions : (1) Question No. 33 to 39.
(2) Attempt any 5 out of 7 questions.
(3) Each question carries 20 marks.
(4) Answer should be given approximately in 200 words.

34. Define central limit theorem. Prove CLT as a generalization of law of large numbers. Mention some of its applications.

35. Distinguish between ‘defect’ and ‘defectives’. Give some examples of defects, for which C-chart is applicable. How do you calculate control limits for a C-chart ? Discuss the assumption and approximations involved in the calculation.

36. Define a 22 factorial experiment. Show that for 22 factorial experiment, the main effects and interaction effects are mutually orthogonal.
37. Define Likelihood Ratio Test (LRT). Obtain LRT for comparing the means of K homoscedastic normal distributions. Mention the asymptotic property of LRT.

38. Define stratified random sampling. In usual notations, show that Var(–yst) is minimum for fixed total size of the sample (n) if ni ? NiSi. Mention its limitations. Obtain the formula for Var(–yst).

39. List out the properties of operators ? and E. Prove an argument that these operators are linear. Why do we need divided differences ? Obtain Newton’s forward interpolation formula as a particular case of Newton’s divided difference formula.