# 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

### Describe in Detail

x_{1 }, 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

### 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

### 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

### 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

### 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

### 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 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.95 |

f | 0.05 | 0.04 | 0.03 | 0.02 | 0.01 | 0.85 |

### Explanation

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