IGNOU MST 21 SOLVED ASSIGNMENT

Included:

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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