Q1. Suppose the probability mass function of a random variable X under the parameter θ = θ_0 and θ = θ_1, θ_1 ≠ θ_0 is given by
- (a) a most powerful test at level 0.05
- (b) a biased test
- (c) test with power 0.90
- (d) test of size 0.01
IES ISS 2020 Statistics Paper II Question Paper PDF | UPSC
- Year 2020
- Conducted By UPSC
- Questions 80
- Maximum Marks 200
- Duration Two Hours
Exam Details
| Detail | Information |
|---|---|
| Examination | Indian Economic Service - Indian Statistical Service Examination |
| Year | 2020 |
| Conducting Body | UPSC |
| Paper | Statistics Paper II |
| Subject | Statistics |
| Duration | Two Hours |
| Maximum Marks | 200 |
| Number of Questions | 80 |
| Question Type | Objective (MCQ) |
This is the Statistics Paper II from the Indian Economic Service - Indian Statistical Service Examination held in 2020, conducted by UPSC. The paper consists of 80 objective-type questions and is allocated a total of 200 marks, with a time limit of two hours. This question paper is crucial for aspirants preparing for the IES ISS exam, offering valuable insights into the exam's structure, the types of questions asked, and the difficulty level. Practicing with previous years' papers like this one helps candidates identify their strengths and weaknesses, refine their preparation strategy, and improve their time management skills for the actual examination.
Major Topics Covered
- Hypothesis Testing
- Likelihood Ratio Test
- Statistical Inference
- Probability Distributions
- Random Variables
- Test Functions
- Power of a Test
- Size of a Test
- Unbiased Test
- Consistent Estimator
- Efficient Estimator
- Sufficient Estimator
Why This Paper is Important
- Useful for Indian Economic Service - Indian Statist 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 2021 Statistics Paper II
- IES ISS 2019 Statistics Paper II
- IES ISS 2020 Statistics Paper I
- UPSC Statistics Optional Papers
- IES ISS 2020 Statistics Paper II Answer Key
- IES ISS Statistics Syllabus
- UPSC Exam Syllabus
- IES ISS Exam Pattern
Instructions
- IMMEDIATELY AFTER THE COMMENCEMENT OF THE EXAMINATION, YOU SHOULD CHECK THAT 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.
- Penalty for wrong answers: 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 has been given by the candidate, one-third of the marks assigned to that question will be deducted as (i) penalty.
- (ii) If a candidate gives more than one answer, it will be treated as a wrong answer even if one of the given 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
Questions (page 2)
Q2. Consider the distribution having probability density function of a random variable X as
- (a) size of the test is 0 and test is unbiased
- (b) size of the test is 1/2 and test is unbiased
- (c) size of the test is 1/3 and test is biased
- (d) size of the test is 1/3 and test is unbiased
Q3. Let X be a random variable with pmf under H0 and H1 given by
- (a) \varphi(x) is a most powerful test of level α = 0.03
- (b) \varphi(x) is a most powerful test of level α = 0.03 with power 0.0975
- (c) \varphi(x) has size 0.0225 and power 0.0975 but it is not a most powerful test with level α = 0.03
- (d) \varphi(x) is not a most powerful test of level α = 0.0225
Q4. Which one of the following parameters is correct in case of Likelihood Ratio Test (LRT)?
- (a) In LRT, control is not affected over the probabilities of type-I error by suitably choosing the cut-off point λ_0
- (b) LRT always gives unbiased test
- (c) When null hypothesis is composite, the LR critical region will be always similar
- (d) Under certain assumptions, an LRT will be consistent
Q5. An estimator to be a good estimator,
- (a) should be efficient but not necessarily unbiased
- (b) should be consistent but not necessarily efficient
- (c) should be unbiased but not necessarily sufficient
- (d) should be unbiased, consistent, sufficient and efficient
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Frequently asked questions
What is the name of the exam for which this paper was conducted?
This paper is from the Indian Economic Service - Indian Statistical Service Examination.
Which year is this question paper from?
This question paper is from the year 2020.
Who conducted the Indian Economic Service - Indian Statistical Service Examination in 2020?
The examination was conducted by UPSC (Union Public Service Commission).
What is the subject of this paper?
The subject of this paper is Statistics, specifically Paper II.
What is the total number of marks for Statistics Paper II?
The maximum marks for Statistics Paper II is 200.
What is the time duration allowed for this paper?
The time allowed for this paper is Two Hours.