IGNOU MST-21 Classical and Bayesian Inference - IGNOU Solved Assignment (Latest)

IGNOU MST-21 (January 2026 – December 2026) Assignment Questions

1. State whether the following statements are True or False. Give reasons in support of your answer:

(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 𝜎𝜎2 = 16. Derive the likelihood ratio test for testing

3. Suppose the number of breakdowns per month in a factory follows a Poisson distribution with parameter 𝜆.

(i) Find the Cramér–Rao lower bound for an unbiased estimator of 𝜆.
(ii) Obtain the UMVUE of 𝜆.

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. Two independent groups of patients were given Drug X and Drug Y. The recovery times (in days) are as follows:

(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.

6. Differentiate between classical and Bayesian estimation.

IGNOU MST-21 (January 2025 – December 2025) Assignment Questions

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 α 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 (n,θ) where θ is the probability of getting spam email, then find the posterior distribution of θ 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

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:

IGNOU MST-21 (June 2024 – June 2025) Assignment Questions

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 α 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) A radar system uses radio waves to detect aircraft. The system receives a signal and based on the received signal, it needs to decide whether an aircraft is present or not. If X denotes the received signal then