# ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 1 - 7 of 39

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## Question number: 1

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Distinguish between the single sampling plan and double sampling plan. Discuss how the O. C curves can be used for comparing two sampling plans.

### Explanation

A single sampling plan in which a decision about the acceptance or rejection of a lot is based on one sample that has been inspected where double sampling plan when a decision about the acceptance or rejection of a lot has not been reached after single sample inspection from a submitted lot, a decision will always be reached when the second sampl

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## Question number: 2

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Derive the likelihood ratio test for comparing the means of k independent homoscedastic normal populations.

### Explanation

Given that there are k independent homoscedastic normal populations that is the variance is same i. e. ; i = 1,2, …, k. We have to test

In the X population the sample is = { (x i1, x i2, …, x ini

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## Question number: 3

» Estimation » Optimal Properties » Complete Statistics

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

Define completeness. Verify whether Bin (1, p) is complete.

### Explanation

Completeness: It is a property of a statistic in relation to a model for a set of observed data. In essence, it is a condition which ensures that the parameters of the probability distribution representing the model can all be estimated on the basis of the statistic: it ensures that the distributions corresponding to different values of the parame

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## Question number: 4

» Estimation » Estimation Methods » Methods of Moments

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

For the Pareto distribution with pdf

Show that method of moments fails if 0 < λ < 1. State the method of moments estimator when λ > 1. Is it consistent? Justify your answer.

### Explanation

Let X 1 , X 2 , …, X n be a simple random sample of Pareto random variables with density

The mean and variance are respectively

In this we have only one parameter λ. Thus, we will o

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## Question number: 5

» Estimation » Estimation Methods » Methods of Moments

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

X 1, X 2, …, X n be a random sample from U (0, θ). Obtain the moment estimator of θ. Also find its variance.

### Explanation

Let X 1, X 2, …, X n be a random sample from U (0, θ). We known that

The estimating equation is

The above equation is solving for the parameter, we get the estimator by using method of moments

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## Question number: 6

» Linear Models » Theory of Linear Estimation » Gauss-Markoff Setup

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

Define estimability of a linear parametric function in a Gauss Markov model. State and prove a necessary and sufficient condition for estimability.

### Explanation

Estimability : The linear parametric function c’β is an estimable function if there exists a vector

a R n such that

If X is of full column rank then all linear combinations of β are estimable, since is unique, that is

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## Question number: 7

» Estimation » Estimation Methods » Maximum Likelihood

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

X 1 , X 2 , …, X n are i. i. d. random variables from N (θ, 1) where θ is an integer. Obtain MLE of θ.

### Explanation

X 1 , X 2 , …, X n are i. i. d. random variables from N (θ, 1). The density function of X is

The likelihood function is

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