# ISS Statistics Paper II (Old Subjective Pattern): Questions 1 - 8 of 39

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## Question number: 1

» Statistical Quality Control » Sequential Sampling Plans

Appeared in Year: 2015

### 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… (282 more words) …

## Question number: 2

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2015

### 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

… (806 more words) …

## Question number: 3

» Estimation » Optimal Properties » Complete Statistics

Appeared in Year: 2014

### 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… (541 more words) …

## Question number: 4

» Estimation » Estimation Methods » Methods of Moments

Appeared in Year: 2014

### 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

… (197 more words) …

## Question number: 5

» Estimation » Estimation Methods » Methods of Moments

Appeared in Year: 2014

### 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

… (137 more words) …

## Question number: 6

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

Appeared in Year: 2014

### 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… (226 more words) …

## Question number: 7

» Estimation » Estimation Methods » Maximum Likelihood

Appeared in Year: 2014

### 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… (183 more words) …

## Question number: 8

» Hypotheses Testing » Hypothesis » Composite

Appeared in Year: 2014

### Describe in Detail

A sample of size n from normal distribution N (θ, σ ^{2 }) with σ ^{2 } =4 was observed. 95 % confidence interval for θ was computed from the above sample. Find the value of n if the confidence interval is (9.02, 10.98).

### Explanation

The Margin of error is defined as

Where z _{α/2 } is the critical value = 1.96

σ is the standard deviation = 2

E is the margin of error= … (51 more words) …