What is the nature of the questions in this paper?

The questions are of the objective type.

Is there any penalty for wrong answers?

Yes, there will be a penalty for wrong answers marked by a candidate. One-third of the marks assigned to that question will be deducted as penalty.

What happens if a candidate gives more than one answer to a question?

If a candidate gives more than one answer, it will be treated as a wrong answer and will incur the same penalty as a single wrong answer.

Is there any penalty for leaving a question blank?

No, if a question is left blank, there will be no penalty for that question.

What should a candidate do if the test booklet has missing or torn pages?

If the test booklet does not have any unprinted or torn or missing pages or items, etc., the candidate should get it replaced by a complete test booklet.

What is the Test Booklet Series Code mentioned?

The Test Booklet Series Code mentioned is BGSP-B-STS.

Let $X_1, X_2, X_3, dots, X_n sim N(\mu, \sigma^2)$ where mean $\mu$ and variance $\sigma^2$ are unknown. Let $S^2 = \frac{1}{n} \sum_{i=1}^{n} (X_i - \bar{X})^2$ and $s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})^2$. Which one of the following is correct according to the efficiency criterion ?

(a) $s^2$ is more efficient than $S^2$.

(b) $s^2$ is less efficient than $S^2$.

(c) $s^2$ and $S^2$ cannot be compared.

(d) Efficiency of $s^2$ is equal to efficiency of $S^2$.

Suppose $X_1, X_2, X_3, dots, X_n$ be a random sample of size n from Poisson distribution with parameter $\lambda$. Then uniformly minimum variance unbiased estimator (UMVUE) of $\lambda$ is :

(a) $\frac{\sum_{i=1}^{n} X_i^2}{n}$

(b) $\frac{\sum_{i=1}^{n} X_i}{n+1}$

(c) $\frac{\sum_{i=1}^{n} X_i}{n}$

(d) $\frac{\sum_{i=1}^{n} X_i^2}{n+1}$

Let S be the set of all unbiased estimators T of $\theta \in \Theta$ such that $E_{\theta}T^2 < \infty$ for all $\theta \in \Theta$. An estimator $T_0 \in S$ is called a uniformly minimum variance unbiased estimator (UMVUE) of $\theta$ for T $\in$ S if :

(a) $E_{\theta}(T_0 - \theta)^2 \le E_{\theta}(T - \theta)^2$

(b) $E_{\theta}(T_0 - \theta)^2 > E_{\theta}(T - \theta)^2$

(c) $E_{\theta}(T_0 - \theta) > E_{\theta}(T - \theta)$

IES ISS 2025 Statistics Paper II Question Paper PDF | UPSC

Name: IES ISS 2025 Statistics Paper II Question Paper PDF | UPSC
Creator: UPSC
Keywords: IES ISS 2025 Statistics Paper II, UPSC Statistics Paper II 2025, Indian Statistical Service 2025 Statistics, Indian Economic Service 2025 Statistics, Statistics Paper II Question Paper PDF

Central Government Jobs Other Jobs 2025

Year 2025
Conducted By UPSC
Questions 80
Maximum Marks 200
Duration Two Hours
Languages English

Exam Details

Detail	Information
Examination	Indian Economic Service - Indian Statistical Service Examination
Year	2025
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 Statistics Paper II for the Indian Economic Service - Indian Statistical Service Examination conducted by UPSC in 2025. The paper is objective in nature, carrying a maximum of 200 marks and a time duration of two hours. It comprises 80 questions, with a penalty for wrong answers. Aspirants can use this question paper to understand the exam pattern, difficulty level, and important topics covered in Statistics Paper II, aiding their preparation strategy.

Major Topics Covered

Statistics
MLE
Unbiased Estimator
Consistent Estimator
Poisson Distribution
UMVUE
Efficiency Criterion

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 2025 Statistics Paper I
IES ISS 2025 General Studies Paper
IES ISS 2024 Statistics Paper II
IES ISS 2025 Statistics Paper II Answer Key
IES ISS Statistics Syllabus
UPSC Exam Syllabus
IES ISS Exam Pattern
UPSC Exam Pattern

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

Questions (page 2)

Q1. Consider the following statements:
I. MLEs are unbiased but not necessarily unique.
II. Unbiased estimator is always unique.
III. If U and W are consistent estimators of θ_1 and θ_2, then UW is also consistent for θ_1θ_2.
Which of the statements given above is/are correct?

(a) I and II
(b) I and III
(c) II and III
(d) III only

Q2. With the increase in sample size if the estimator becomes closer and closer to the parameter, then it is called :

(a) Completeness
(b) Consistent
(c) Sufficient
(d) Unbiasedness

Q3. Let X₁, X₂, X₃, dots, X_n sim N(μ, σ^2) where mean μ and variance σ^2 are unknown. Let S² = (1)/(n) ∑_i=1ⁿ (X_i - \barX)^2 and s² = (1)/(n-1) ∑_i=1ⁿ (X_i - \barX)^2.
Which one of the following is correct according to the efficiency criterion ?

(2) BGSP-B-STS

(a) s² is more efficient than S².
(b) s² is less efficient than S².
(c) s² and S² cannot be compared.
(d) Efficiency of s² is equal to efficiency of S².

Q4. Suppose X₁, X₂, X₃, dots, X_n be a random sample of size n from Poisson distribution with parameter λ. Then uniformly minimum variance unbiased estimator (UMVUE) of λ is :

(a) (∑_i=1ⁿ X_i^2)/(n)
(b) (∑_i=1ⁿ X_i)/(n + 1)
(c) (∑_i=1ⁿ X_i)/(n)
(d) (∑_i=1ⁿ X_i^2)/(n + 1)

Q5. Let S be the set of all unbiased estimators T of θ ∈ \Theta such that E_θT² < ∞ for all θ ∈ \Theta. An estimator T₀ ∈ S is called a uniformly minimum variance unbiased estimator (UMVUE) of θ for T ∈ S if :

(a) E_θ(T₀ - θ)² ≤ E_θ(T - θ)²
(b) E_θ(T₀ - θ)² > E_θ(T - θ)²
(c) E_θ(T₀ - θ) > E_θ(T - θ)

Q6. Let X₁, X₂, X₃, dots, X_n be a random sample from N(μ, σ^2). Consider the statistic s² = (1)/(n-1) ∑_i=1ⁿ (X_i - \barX)^2. What is V(s²) equal to ?

(a) (2σ^4)/(n-1)
(b) (2σ^2)/(n-2)
(c) (2σ^2)/(n-1)
(d) (2σ)/(n-1)

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Frequently asked questions

What is the name of the examination?

The examination is the Indian Economic Service - Indian Statistical Service Examination.

Which paper is this question booklet for?

This is for Statistics Paper II.

What is the conducting body for this exam?

The exam is conducted by UPSC.

What is the maximum marks for Statistics Paper II?

The maximum marks for Statistics Paper II is 200.

What is the time allowed for this paper?

The time allowed for Statistics Paper II is Two Hours.

How many questions are there in Statistics Paper II?

There are 80 items (questions) in this Test Booklet.

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