IGNOU MSCAST MST 21 Classical and Bayesian Inference Solved Assignment ENGLISH
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MST 21: Classical and Bayesian Inference
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| Title Name | IGNOU MSCAST MST 21 Classical and Bayesian Inference Solved Assignment ENGLISH |
|---|---|
| Type | Soft Copy (E-Assignment) .pdf |
| University | IGNOU |
| Degree | MASTER DEGREE PROGRAMMES |
| Course Code | MSCAST |
| Course Name | M.Sc. (Applied Statistics) |
| Subject Code | MST 21 |
| Subject Name | Classical and Bayesian Inference |
| Year | 2026 |
| Session | - |
| Language | ENGLISH |
| Assignment Code | MST 21/Assignment-1/2026 |
| Product Description | Assignment of MSCAST (M.Sc. (Applied Statistics)) 2026. Latest MST 021 2026 Solved Assignment Solutions |
| Format | Ready-to-Print PDF (.soft copy) |
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MST 021 (January 2026 - July 2026) - ENGLISH
Course Code: MST-021
Assignment Code: MST-021/TMA/2026
Maximum Marks: 100
Note: All questions are compulsory. Answer in your own words.
1. State whether the following statements are True or False. Give reasons in support of your answer:
(5×2=10)
(i) When the population distribution is unknown and the data are measured on a nominal scale, the Sign test can be used to test a hypothesis about the median.
(ii) In the Bayesian framework, prior information about the parameter is combined with the likelihood to obtain the posterior distribution.
(iii) The Wilcoxon rank-sum test is a non-parametric alternative to the two-sample t-test when normality is not assumed.
(iv) A complete sufficient statistic guarantees the uniqueness of the unbiased estimator obtained through it.
(v) The power of a statistical test is the probability of accepting the null hypothesis when it is true.
2. A pharmaceutical company fills medicine bottles with a target weight of 500 mg. It is known that the filling weights are normally distributed with known variance o² = 16. Derive the likelihood ratio test for testing
Ηο: μ = 500againstH₁: μ ≠ 500
at significance level a.
3. Suppose the number of breakdowns per month in a factory follows a Poisson distribution with parameter λ.
(i) Find the Cramer-Rao lower bound for an unbiased estimator of λ.
(ii) Obtain the UMVUE of λ.
(i) Find the Cramer-Rao lower bound for the variance. (ii) Also, find the UMVUE of $lambda$. (20)
5. Two independent groups of patients were given Drug X and Drug Y. The recovery times (in days) are as follows:
| Drug X | 8 | 10 | 9 | 7 | 11 |
| Drug Y | 6 | 7 | 5 | 8 | 6 |
(i) State the null and alternative hypotheses.
(ii) Explain why the Mann–Whitney U test is appropriate for this data.
(iii) Perform the test at the 5% level of significance and draw a conclusion. (20)
6. Differentiate between classical and Bayesian estimation. (10)
MST 021 (January 2025 - July 2025) - ENGLISH
TUTOR MARKED ASSIGNMENT
MST-021: Classical and Bayesian Inference
Course Code: MST-021
Assignment Code: MST-021/TMA/2025
Maximum Marks: 100
Note: All questions are compulsory. Answer in your own words.
1(a) State whether the following statements are True or False. Give reasons in support of your answer:
(i) If the form of the population is not known and data are in ordinal form then we apply the Wilcoxon Signed rank test for testing hypothesis about average.
(ii) The Neyman-Pearson lemma provides the most powerful test of size a for testing a simple hypothesis against a simple alternative hypothesis.
(iii) The Rao-Blackwell theorem enables us to obtain a manimum variance unbiased estimator through complete statistic.
(iv) For testing goodness of fit when the data are in categorical form, we use K-S test.
(v) In the Bayesian approach, we treat the parameter as a constant.
(b) Differentiate between Rao-Blackwell and Lehmann-Scheffe theorems.
2. A faculty member of a university receives a number of emails. If X represents the number of spam emails in n emails and follows a binomial distribution with parameters where
is the probability of getting spam email, then find the posterior distribution of considering the following beta distribution.
Also, find the posterior mean of θ .
3. A food processing company packages 10 gm of honey in small jars. Previous experience suggests that the volume of a randomly selected jar of the company’s honey is normally distributed with a known variance of 2 gm. Drive likelihood ratio test for testing
at a α level of significance. Given
4. If the number of weekly accidents occurring on a mile stretch of a particular road follows a Poisson distribution with parameter λ . Then
(i) Find the Cramer-Rao lower bound for the variance.
(ii) Also, find the UMVUE of λ .
5. The following data give the sales of 6 models of mobiles at four different stores. The sales of each mobile (in number of mobiles sold) from each store are given as follows:
| Store A | Store B | Store C | Store D |
| 58 | 74 | 35 | 78 |
| 55 | 57 | 51 | 85 |
| 38 | 65 | 41 | 62 |
| 63 | 48 | 52 | 75 |
| 41 | 83 | 54 | 87 |
| 50 | 61 | 53 | 57 |
Test whether there is a significant difference in the sales of the four stores by using the Kruskal Wallies test at 1% level of significance
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Course: M.Sc. (Applied Statistics) (MSCAST)
Subject: MST 21 - Classical and Bayesian Inference
Session: January 2026 - December 2026
Language: ENGLISH
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Product Information
| Course Name | M.Sc. (Applied Statistics) |
| Course Code | MSCAST |
| Subject Code | MST 21 |
| Subject | Classical and Bayesian Inference |
| Programme | MASTER DEGREE PROGRAMMES Courses |
| Language | ENGLISH |
| Material Type | Solved Assignment – Soft Copy / PDF |
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