IES ISS Exam 2022 Statistics Paper II Question Paper PDF

Central Government Jobs Other Jobs 2022

  • Year 2022
  • Conducted By UPSC
  • Questions 80
  • Maximum Marks 200
  • Duration Two Hours

Exam Details

Detail Information
Examination IES/ISS Exam
Year 2022
Conducting Body UPSC
Paper Statistics Paper II
Subject Statistics
Duration Two Hours
Maximum Marks 200
Number of Questions 80
Question Type Objective (MCQ)

This document contains the official question paper for the IES/ISS Exam 2022, specifically for Statistics Paper II, conducted by UPSC. The exam allows two hours to complete and is worth a maximum of 200 marks. It is designed for candidates aspiring to join the Indian Statistical Service or Indian Economic Service. Aspirants can use this paper to understand the exam's objective question format, difficulty level, and the specific statistical concepts tested, aiding in their preparation strategy.

Major Topics Covered

  • Statistics
  • Linear Models
  • Estimation
  • Generalized Inverses
  • Moore-Penrose Inverse
  • BLUEs (Best Linear Unbiased Estimators)
  • MLEs (Maximum Likelihood Estimators)
  • Probability Distributions
  • Regression Analysis

Why This Paper is Important

  • Useful for IES/ISS Exam preparation
  • Helps understand the latest exam pattern
  • Useful for practice and self-assessment
  • Covers frequently asked General Studies topics
  • Helpful for analysing question trends

Related Resources

  • IES ISS Exam 2021 Statistics Paper II
  • IES ISS Exam 2023 Statistics Paper II
  • UPSC Statistics Paper I 2022
  • Statistical Officer Previous Year Papers
  • IES ISS Exam 2022 Statistics Paper II Answer Key
  • IES ISS Exam Syllabus
  • Statistics Syllabus for UPSC Exams
  • Indian Statistical Service Syllabus

Instructions

  • THIS TEST BOOKLET DOES NOT HAVE ANY UNPRINTED OR TORN OR MISSING PAGES OR ITEMS, ETC.
  • IF SO, GET IT REPLACED BY A COMPLETE TEST BOOKLET.
  • Please note that it is the candidate's responsibility to encode and fill in the Roll Number and Test
  • Booklet Series Code A, B, C or D carefully and without any omission or discrepancy at the appropriate places in the OMR Answer Sheet.
  • Any omission/discrepancy will render the Answer Sheet liable for rejection.
  • You have to enter your Roll Number on the
  • Test Booklet in the Box provided alongside.
  • DO NOT write anything else on the Test Booklet.
  • This Test Booklet contains 80 items (questions).
  • Each item comprises four responses (answers).
  • will select the response which you want to mark on the Answer Sheet.
  • In case you feel that there is more than one correct response, mark the response which you consider the best.
  • In any case, choose ONLY ONE response for each item.
  • You have to mark all your responses ONLY on the separate Answer Sheet provided.
  • in the Answer Sheet. All items carry equal marks.
  • Before you proceed to mark in the Answer Sheet the response to various items in the Test Booklet,
  • you have to fill in some particulars in the Answer Sheet as per instructions sent to you with your Admission Certificate.
  • After you have completed filling in all your responses on the Answer Sheet and the examination has
  • concluded, you should hand over to the Invigilator only the Answer Sheet.
  • You are permitted to take away with you the Test Booklet.
  • Sheets for rough work are appended in the Test Booklet at the end.
  • THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE IN THE OBJECTIVE TYPE QUESTION PAPERS.
  • There are four alternatives for the answer to every question.
  • For each question for which a wrong answer (i) has been given by the candidate, one-third of the marks assigned to that question will be deducted as penalty.
  • If a candidate gives more than one answer, it will be treated as a wrong answer even if one of the given (ii) answers happens to be correct and there will be same penalty as above to that question.
  • If a question is left blank, i.e., no answer is given by the candidate, there will be no penalty for that (iii) question.
  • DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO (1-A)

Questions (page 2)

Q1. Let Y = Xβ + \varepsilon, where Y is n imes 1 vector of response, X is n imes k (n > k) matrix of predictors, β is k imes 1 vector of unknown coefficients to be estimated and \varepsilon is n imes 1 vector of random errors. Further \varepsilon is N(0, σ^2 I). The distribution of \hatY is :

  • (a) N(Xβ, σ^2)
  • (b) N(Xβ, X(X'X)-1 X'σ^2)
  • (c) N(Xβ, (X'X)-1 σ^2)
  • (d) N(Xβ, (X'X)-1 X'σ^2)

Q2. An ecologist takes data (Xi, Yi); i = 1, 2, 3, . . n where Xi is the size of an area and Yi is the number of moss plants in the area. We model the data by Yi sim Poisson (θ xi); Yi's are independent. The least square estimator and the MLE of θ are respectively :.

  • (a) (∑i=1n Yi)/(∑i=1n Xi), (∑i=1n Xi Yi)/(∑i=1n Xi^2))
  • (b) (∑i=1n Xi Yi)/(∑i=1n Xi^2), (∑i=1n Yi)/(∑i=1n Xi))
  • (c) (\overlineY)/(\overlineX), (\textCov(X, Y))/(V(X)))
  • (d) (\textCov (X, Y))/(V(X)), (\overlineY)/(\overlineX))

Q3. Let A be any n imes m matrix with A^- as any generalized inverse of it. Further, let H = AA^- and T = A^{-}A. Then which one of the following is correct?

  • (a) Only H is an idempotent matrix
  • (b) Only T is an idempotent matrix
  • (c) Both H and T are idempotent matrices
  • (d) Neither H nor T is an idempotent matrix

Q4. Let A be a matrix of order n imes p with A^- as any generalized inverse of it. Let (A'A)^- be any generalized inverse of A'A, then which of the following are correct?

  • (1) (A^{-})' = (A')^{-}
  • (2) A^- = (A'A)^- A'
  • (3) Rank(A'A) = rank(AA^{-})
  • (a) 1 and 2 only
  • (b) 2 and 3 only
  • (c) 1 and 3 only
  • (d) 1, 2 and 3

Q5. Let A be any matrix of order n imes m. Consider the following statements for its Moore-Penrose inverse A^+:

  • (1) A^+ = (A'A)^+ A'
  • (2) A^+ is unique
  • (a) 1 only
  • (b) 2 only
  • (c) Both 1 and 2
  • (d) Neither 1 nor 2

Q6. Let Xi, Yi and Zi; i = 1, 2, 3 be nine independent observations with common variance σ^2, and E(Xi) = θ_1, E(Yi) = θ_2, E(Zi) = θ_1 - θ_2; i = 1, 2, 3. If \hatθ_1 and \hatθ_2 denote the BLUEs of θ_1 and θ_2 respectively, then which one of the following is correct ?

  • (a) V(\hatθ_1) > V(\hatθ_2)
  • (b) V(\hatθ_1) = V(\hatθ_2)
  • (c) V(\hatθ_1) < V(\hatθ_2)
  • (d) V(\hatθ_1) ≥ V(\hatθ_2)

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Frequently asked questions

What is the name of the exam?

The exam is the IES/ISS Exam.

What year is this question paper from?

This question paper is from the year 2022.

Who conducts the IES/ISS Exam?

The IES/ISS Exam is conducted by UPSC (Union Public Service Commission).

What is the subject of this paper?

This paper is for Statistics, specifically Paper II.

What is the total time allowed for the exam?

The time allowed for this paper is Two Hours.

What are the maximum marks for Statistics Paper II?

The maximum marks for Statistics Paper II are 200.

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