Statistics Paper I 2025 – Maharashtra MSS Main Exam (Section A)
- Year 2025
- Conducted By Government of Maharashtra
- Questions 8
- Maximum Marks 250
- Duration Three Hours
- Languages English
Exam Details
| Detail | Information |
|---|---|
| Examination | Maharashtra State Services Main Examination |
| Year | 2025 |
| Conducting Body | Government of Maharashtra |
| Paper | Statistics Paper - I |
| Subject | Statistics |
| Duration | Three Hours |
| Maximum Marks | 250 |
| Number of Questions | 8 |
| Question Type | Mixed |
Page 1 provides the exam header for Maharashtra State Services Main Examination, Statistics Paper I (C23). It notes English medium, three-hour duration, 250 maximum marks, and eight total questions across two sections, with Question 1 and 5 compulsory. Page 2 presents Section A (5 × 10 = 50) containing Q1 with subparts (a)–(e). Subpart (a) contains an urn-proportion probability problem followed by a two-dice probability setup. Subpart (b) presents options related to the dice probability. Subpart (c) covers estimator theory: unbiasedness and selection of the best estimator among t1, t2, t3. Subpart (d) involves the mean and MVUE for an exponential distribution. Subpart (e) asks for the MLEs of μ (known σ^2) and σ^2 (known μ) for a normal model. This document compiles corrected OCR content and organizes questions for SEO-ready metadata, FAQs, and image optimization cues.
Major Topics Covered
- Statistics
- Probability
- Estimation
- Unbiasedness
- MVUE
- Maximum Likelihood Estimation
- Normal Distribution
- Exponential Distribution
- Random Sampling
- Descriptive Statistics
- Sampling Theory
- Bayes
- Hypothesis Testing
- Point Estimators
- Variance
- Conditional Probability
- Discrete Probability
- Continuous Probability
- Joint Distributions
- Inference
Why This Paper is Important
- Useful for Maharashtra State Services Main Examinat 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
Instructions
- 2ाज्य प्रेम (ग्रुम) परीक्षा-2,24 परीक्षा दिनौक ०२ में, 2026 2025 C23 BOOKLET NO. 174001 Statistics Paper - I Time Allowed: Three Hours Maximum Marks: 250 Type of Paper : Conventional/Descriptive Medium : English
- There are EIGHT questions divided in two Sections, out of which FIVE are to be attempted.
- Question No. 1 and 5 are compulsory.
- Out of the remaining, THREE are to be attempted choosing at least ONE question from each Section. \ast SE З.
- The number of marks carried by a question/sub-question is indicated against it.
- The medium of answer should be mentioned on the answer book as claimed in the application and printed on admission card.
- The answers written in medium other than the authorized medium will not be assessed and no marks will be assigned to them.
- Wherever option has been given, only the required number of responses in the serial order attempted shall be assessed.
- Unless struck off, attempt of a question shall be counted even if attempted partly.
- Excess responses shall not be assessed and shall be ignored.
- Candidates are expected to answer all the sub-questions of a question together.
- If sub-question of a question is attempted elsewhere (after leaving a few page or after attempting another question) the later sub-question shall be overlooked.
- Keep in mind the word limit indicated in the question if any.
- Any page or portion of the page left blank in the Answer Bookiet must be clearly struck off.
- Unless otherwise mentioned, symbol and notation have their usual standard meanings.
- Assume suitable data, if necessary and indicate the same clearly.
- Neat sketches may be drawn, wherever required.
- Note: Candidates will be allowed to use Scientific (Non-programmable type) calculators.
Questions (page 2)
Q2. Q1. (b) [Options listed below correspond to the probability event in the preceding stem.]
Q3. A random sample (X1, X2, X3, X4, X5) of size 5 is drawn from a normal population with unknown mean μ, consider the following estimators to estimate μ: t1 = (X1 + X2 + X3 + X4 + X5)/5, t2 = (X1 + X2)/2 + X3 and t3 = (2X1 + X2 + λ X3)/3, where λ is such that t3 is an unbiased estimator of μ. Find λ. Are t1 and t2 unbiased? State, giving reasons, the estimator which is best among t1, t2 and t3.
Q4. Show that X̄ = (1/n) ∑_{i=1}^{n} Xi in random sampling from f(x, θ) = { (1/θ) exp(-x/θ) , 0 < x < ∞ ; 0 otherwise } where 0 < θ < ∞, is an MVUE of θ and has variance θ^2/n.
Q5. In random sampling from normal population N(μ, σ^2), find the maximum likelihood estimator for i) μ when σ^2 is known, and ii) σ^2 when μ is known.
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Frequently asked questions
How many questions are in the exam and how many are to be attempted?
There are eight questions in two sections; five questions must be attempted.
Which questions are compulsory?
Question No. 1 and Question No. 5 are compulsory.
What is the duration of the examination?
Three hours.
What is the maximum marks for the paper?
Maximum marks are 250.
In what language is the paper conducted?
Medium: English.
What is Section A about?
Section A contains five subparts of Question 1 (Q1(a)–Q1(e)) worth 50 marks in total.