# Estimation (ISS Statistics Paper II (Old Subjective Pattern)): Questions 1 - 7 of 14

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to **39** questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 200.00 or

## Question number: 1

» 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: 2

» 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: 3

» 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: 4

» 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: 5

» Estimation » Optimal Properties » Sufficient Estimator

Appeared in Year: 2014

### Describe in Detail

Show that is not a sufficient estimator of the Bernoulli parameter θ.

### Explanation

Let X _{i } is a ith random variable follows Bernoulli distribution with parameter θ. Then, the random variable is defined as

… (195 more words) …

## Question number: 6

» 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

Let x _{1 }, x _{2 }, …, x _{n } be a random sample from f (x, α) and let L (α| x) denote the likelihood function. Then

… (144 more words) …

## Question number: 7

» 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

… (82 more words) …