HCS Statistics Mains 2022 – OCR Repair
- Year 2022
- Questions 8
- Maximum Marks 200
- Duration 3 Hours
Exam Details
| Detail | Information |
|---|---|
| Examination | Statistics |
| Year | 2022 |
| Paper | Statistics |
| Subject | Statistics |
| Duration | 3 Hours |
| Maximum Marks | 200 |
| Number of Questions | 8 |
This OCR-repaired page set corresponds to the Statistics paper for the Haryana Civil Services (Ex.Br.) & Other Allied Services Mains Exam 2022. Page 1 presents the exam header, duration (3 hours), maximum marks (200), and language instructions in English and Hindi, confirming a two-section layout with four questions per section and a requirement to attempt five questions in total, with questions 1 and 5 compulsory. Page 2 (Section A) contains descriptive subparts for Q1: (a) a probability problem with X1, X2 ~ N(0,1); (b) a goodness-of-fit style die-rolling problem to determine b given a 2,3,4,5,6,1 outcome table; (c) a problem on an unbiased estimator of θ from a two-normal mixture pdf; and (d) estimability conditions for a linear function of μ1, μ2, μ3, including normal equations. The OCR-repair clarifies bilingual prompts and formats each subpart distinctly for SEO-friendly extraction.
Major Topics Covered
- Statistics
- Probability
- Random Sampling
- Normal Distribution
- Standard Normal
- Chi-Square Distribution
- Unbiased Estimator
- Estimation
- Estimability
- Linear Models
- Normal Equations
- Hypothesis Testing
- Goodness-of-Fit
- Likelihood
- Parameter θ
- Estimation Techniques
- Linear Combination
- Statistical Inference
- Moments
Why This Paper is Important
- Useful for HCS (Ex.Br.) & Other Allied Services Mai 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
- 2022 Statistics सांख्यिकी Time: 3 hours Maximum Marks: 200 समयः 3 घंटे अधिकतम अंकः 200
- This paper is divided into two Sections, Section-A and Section-B. ये प्रश्नपत्र दो खंडों में विभाजित है, खंड. А और खंड. В ii.
- Each Section contains four (4) questions. प्रत्येक खंड में चार प्रश्न है। iii.
- Candidate has to attempt five questions in all. परीक्षार्थी को पांच प्रश्नों का उत्तर लिखना है। iv.
- Question Nos. 1 and 5 are compulsory and out of the remaining, THREE questions are to be attempted choosing at least ONE question from each Section. प्रश्न संख्या 1 और 5 अनिवार्य है और शेष प्रश्नों में से किन्हीं तीन का उत्तर लिखना है, प्रत्येक खंड से एक प्रश्न को हल करना है। Word limit in questions, where specified, should be adhered to.
- V. प्रश्नों में शब्द सीमा, जहाँ विनिर्दिष्ट है, का अनुसरण किया जाना चाहिए। The number of marks carried by a question/part is indicated against it. vi. प्रत्येक प्रश्न/भाग के लिए नियत अंक उसके सामने दिए गए हैं। Questions are printed in English & Hindi languages.
- In case of any ambiguity in translation of any vii. question, English version shall be treated as final. प्रत्येक प्रश्न हिन्दी और अंग्रेजी दोनों भाषाओं में छपा है। प्रश्नों के अनुवाद में किसी अस्पष्टता की स्थिति में, अंग्रेजी सस्ंकरण को ही अन्तिम माना जाएगा। 1\,
Questions (page 2)
Q2.
1(b). A die was cast independently for 120 times and the following table shows the results.
(8) Spots up: 2 3 4 5 6 1; Frequency: 20 20 20 (40−b) b
20. The hypothesis H0: die is unbiased; is tested and rejected at the level of significance 0.025. Find the value of b. Hindi: एक पासे को 120 बार स्वतंत्र रूप से उछालने पर निम्नलिखित परिणाम प्राप्त हुए।
Spots up: 2 3 4 5 6 1; Frequency: 20 20 20 (40−b) b
20. सार्थकता स्तर 0.025 पर H0: पासा अनभिनत है, को अस्वीकार किया गया है, तो b का मान ज्ञात कीजिए।
Q3.
1
(c) . Let X1, X2, ..., Xn be a random sample of size n from the distribution having p.d.f. f(x|θ) = c( e^{−(x−2θ)^2/2} + e^{−(x−4θ)^2/2} ), −∞ < x < ∞, −∞ < θ < ∞. Find an unbiased estimator of θ. Hindi: X1, X2, ..., Xn ऐसे यादच्छिक प्रतिदर्श हैं जिनका घनत्व फलन f(x|θ) दिया गया है; θ का unbiased estimator ज्ञात कीजिए।
Q4. 1(d). Consider three independent random variables, Y1, Y2 and Y3, having common variance σ^2 and expectations E(Y1) = E(Y3) = μ1 + μ3 and E(Y2) = μ1 + μ2. Determine the condition of estimability of the parametric function μ = l1 μ1 + l2 μ2 + l3 μ3. Obtain the expression for the normal equations. Hindi: तीन स्वतंत्र यादच्छिक चर, Y1, Y2 और Y3, जिनका एक समान प्रसार σ^2 है और प्रत्याशाएँ E(Y1)=E(Y3)=μ1+μ3, E(Y2)=μ1+μ2 हैं, पैरामीट्रिक फ़ंक्शन μ = l1 μ1 + l2 μ2 + l3 μ3 की आंकलनीय होने की शर्त निर्धारित करें। व्यंजक (normal equations) भी पाएं।
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Frequently asked questions
What is the exam name and year?
HCS (Ex.Br.) & Other Allied Services Mains Exam-2022
What is the duration and maximum marks?
3 hours; 200 marks
How many sections and questions are there?
Two sections (Section A and Section B); each contains four questions.
How many questions must a candidate attempt?
Five questions in total, with at least one from each section; questions 1 and 5 are compulsory.
Are the questions printed in English and Hindi?
Yes, questions are bilingual in English and Hindi.
How are marks indicated?
The marks carried by a question/part are indicated against it.