ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 14 - 19 of 39

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Question number: 14

» Estimation » Estimation Methods » Maximum Likelihood

Appeared in Year: 2014

Essay Question▾

Describe in Detail

x1 , x 2 , …, x n be a random sample from the following distribution

Explanation

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Question number: 15

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2014

Essay Question▾

Describe in Detail

x 1 , x 2 , …, x n is a random sample from N (θ, σ 2 ) (σ 2 not specified). Derive likelihood ratio test of testing H 0 : θ=θ 0 against H 1 : θ ≠ θ 0 .

Explanation

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Question number: 16

» Linear Models » Use of G-Inverse

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Obtain a g-inverse of A given below and verify that AA - A = A

Explanation

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Question number: 17

» Hypotheses Testing » Two Kinds of Error

Appeared in Year: 2014

Essay Question▾

Describe in Detail

A single observation of a r. v. having a geometric distribution with pmf

The null hypothesis is H 0 : θ=0.5 against the alternative hypothesis H 1 : θ=0.6 is rejected if the observed value of r. v. is greater than equal to 5. Find the probabilities of type I error and type II error.

Explanation

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Question number: 18

» Hypotheses Testing » Randomised Test

Appeared in Year: 2014

Essay Question▾

Describe in Detail

chart is used to control the mean of normally distributed characteristic. It is know that . The center line is 200. If the process mean shifts to 188, find the probability that this shift is detected on the first subsequent sample.

Explanation

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Question number: 19

» Hypotheses Testing » Most Powerful Test

Appeared in Year: 2014

Essay Question▾

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

Possible X Values given in table

Finding a values of f 0 (x) and f 1 (x) to given a table.

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

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