ISS Statistics Paper II (Old Subjective Pattern): Questions 19 - 23 of 39
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Question number: 19
» Hypotheses Testing » Most Powerful Test
Appeared in Year: 2014
Describe in Detail
Let X be r. v. with pmf under H 0 and H 1 given below. Find M. P. test with α=0.03
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| f 0 (x) | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.95 |
| f 1 (x) | 0.05 | 0.04 | 0.03 | 0.02 | 0.01 | 0.85 |
Explanation
To find the M. P. test, first we compute
| Z | 5 | 4 | 3 | 2 | 1 | 0.8947 |
The possible… (205 more words) …
Question number: 20
» Estimation » Estimation Methods » Maximum Likelihood
Appeared in Year: 2014
Describe in Detail
Let X be exponentially distributed with parameter θ. Obtain MLE of θ based on a sample of size n, from the above distribution.
Explanation
Let X be exponentially distributed with parameter θ.
The likelihood function is
Question number: 21
» Estimation » Optimal Properties » Confidence Interval Estimation
Appeared in Year: 2015
Describe in Detail
Let y 1, y 2, …, y n be a random sample from N (µ, σ 2) where µ and σ 2 are both unknown. Obtain a confidence interval of µ with confidence coefficient (1-α)
Explanation
When population mean and population standard deviation in not know. If is the samplemean and replace σ by its estimate s and t α/2 be the critical value of the student t-test such that have of the area on the left hand side and other half on the… (113 more words) …
Question number: 22
» Estimation » Optimal Properties » Sufficient Estimator
Appeared in Year: 2015
Describe in Detail
Obtain the sufficient statistics for the following distribution.
(i)
(ii)
Explanation
By using factorization theorem, the condition is that
where h (x) is free from θ and g (. ) depends on X only… (268 more words) …
Question number: 23
» Multivariate Analysis » Distribution of Hotelling T2 Statistic » Use for Testing
Appeared in Year: 2015
Describe in Detail
Show that T 2 statistic is invariant under changes in the unit of measurements for a p×1 random vector X of the form Y =C X + d where C is a p×p nonsingular matrix, d is a p×1 vector.
Explanation
T 2 statistic can be computed from X. Here we have to compute it form Y and both will be same. Here
Let , then