The Commission publishes this paper without an answer key, so no answers are shown.
1. Define harmonic mean. (2)
2. What is regression ? (2)
3. State addition theorem on probability for two events. (2)
4. Define normal distribution. (2)
5. State sufficient set of conditions for consistency of an estimator. (2)
6. Define probabilities of type I and type II errors. (4)
7. Write any two properties of moment estimators. (4)
8. Define Karl-Pearson's coefficient of skewness. (4)
9. Define chi-square distribution with n degrees of freedom. (4)
10. Obtain the mean of Poisson distribution with parameter λ. (4)
11. If A and B are two events such that P(A) = 1/3, P(B) = 1/4 and P(A ∩ B) = 1/8, find P(A/B) and P(A/Bᶜ). (5)
12. A continuous random variable X has probability density f(x) = 3x², 0 ≤ x ≤ 1. Find a such that P(X ≤ a) = P(X > a). (5)
13. Explain the best test for a simple hypothesis. (5)
14. Explain the chi-square test for the variance of a normal population. (5)
15. Explain method of moment estimation. (5)
16. State Gauss-Markov theorem. (5)
17. What are the basic assumptions used in analysis of variance ? (5)
18. Define the following :
(a) Test statistic
(b) Critical region
(c) Level of significance
(d) p value. (7)
19. Find the size and power of the following test. Reject H₀: λ = 1 in favour of H₁: λ = 2 whenever X₁ + X₂ ≥ 2. Assume X₁ and X₂ are independent observations from a Poisson distribution with parameter λ. (7)
20. Write any four merits and any three demerits of standard deviation. (7)
21. Explain principle of least squares. (7)
22. Explain paired t test. (7)
23. Explain analysis of variance one way classification. (10)
24. State and prove Baye's theorem. (10)
25. A random sample of size n is taken from a normal population with mean zero and variance σ². Examine whether t = (1/n)Σᵢ₌₁ⁿ Xᵢ² is a minimum-variance-bound unbiased estimator of σ². Hence find Var(t). (10)
26. (1) Explain stratified sampling and what are its merits?
(2) Explain cluster sampling. (10)
27. For the rectangular distribution over the interval (α, β), where α < β. Find the maximum likelihood estimators for α and β. (10)
28. Obtain (1 – α)100% confidence interval for the difference of means of two independent normal populations N(μ₁, σ₁²) and N(μ₂, σ₂²), when σ₁² and σ₂² are known. (10)
29. Explain the t test for testing the equality of means of two normal populations. (10)
30. Explain Chi-square goodness of fit test. (10)
31. Explain the test concerning the mean of a normal population when population variance σ² is known. (10)
32. (a) How can the Shewhart control chart be prepared ?
(b) How to interpret Shewhart control chart ? (10)
Discussion
Ask a doubt or share a tip.
No comments yet — start the discussion.