# ISS (Statistical Services) Statistics Paper III: Questions 91 - 100 of 109

Access detailed explanations (illustrated with images and videos) to **109** questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. *Unlimited Access, Unlimited Time, on Unlimited Devices*!

View Sample Explanation or View Features.

Rs. 300.00 -OR-

How to register? Already Subscribed?

## Question 91

### Describe in Detail

Essay▾What is a Wiener process? Obtain the forward diffusion equation of a Wiener process. Also discuss any two application of the process.

### Explanation

A stochastic process is a random process that is a function of time. Brownian motion is a stochastic process that evolves in continuous time, with movements that are continuous. So, Brownian motion is a continuous stochastic process, Z (t) , with the following characteristics:

- Z (0) = 1
- Z (t) is continuous .
- Z (t + s
_{1}) − Z (t) is independent of Z (t) …

… (283 more words) …

## Question 92

## Question 93

### Describe in Detail

Essay▾Define a Poisson process. Stating the regularity conditions, Show that P_{n} (t) = P {N (t) = n} is given by the Poisson law

### Explanation

Let X (t) denote the number of occurrences of a typical event over [0, t] , X (t) is also referred as a counting process. Let X (t) be non-negative integer values continuous time process. Assume that

- X (t + h) -X (t) is independent of X (t) -X (0) with X (0) = 0 that process with independent increments.
- X (t + h) -X (t) does not depend on t that is X…

… (121 more words) …

## Question 94

### Describe in Detail

Essay▾If X_{n} is a branching process with

and σ^{2} = Var (X_{1}) , then show that

- E (X
_{n}) = m^{n}

### Explanation

Let X_{0} = 1. It is evident

Let Z_{ij} be i. i. d with the offspring distribution P [Z_{ij} = k] = p_{k}, k = 0,1, 2, . . Such a process {X_{n}} is called branching process and X_{n} denotes the number of individual in the nth generation.

(i)

Since these are independent

By the definition of branching process

In the above equation and the process are identical

From equati…

… (25 more words) …

## Question 95

### Write in Short

Short Answer▾What is Gambler՚s ruin problem? Obtain the probability of ruin, if Gambler plays with a capital of a rupees.

## Question 96

### Describe in Detail

Essay▾Define a Galton- Watson branching process. If {p_{k}} is the offspring distribution, then prove the following identities:

(i) P_{n} (s) = P_{n-1} [P (s) ]

(ii) ) P_{n} (s) = P [P_{n-1} (s) ]

### Explanation

Consider a population consisting of individual, able to produce identical offsprings of the same type and dies after producing. Let Z_{ij} be the number of offspring produced by the j^{th} individual of the i^{th} generation and X_{n} be number of individual of the n^{th} generation, j = 1,2, … , X_{i} and i = 0,1, 2, …

Let X_{0} = 1. It is evident

Let Z_{ij} be independent…

… (95 more words) …

## Question 97

### Describe in Detail

Essay▾State and explain various types of data is used in the estimation of the model.

### Explanation

**In the estimation of model the following types of data are used**:

**(I) Time series data**:

Time series data give information about the numerical values of variables from period to period and are collected over time.

For example, the data during the years 1990 - 2010 for monthly income constitutes a time series data.

**(II) Cross section data**:

The cross sectio…

… (185 more words) …

## Question 98

### Explanation

A model is a simplified representation of a real world process. It should be representative in the sense that it should contain the salient features of the phenomena under study.

In general, one of the objectives in modeling is to have a simple model to explain a complex phenomenon. Such an objective may sometimes lead to oversimplified model and so…

… (152 more words) …

## Question 99

## Question 100

### Describe in Detail

Essay▾What are the aims of econometrics? How econometrics differ from economic statistics?

### Explanation

The three main aims of econometrics are as follows:

**(I) Formulation and specification of econometric models**:

The economic models are formulated in an empirically testable form. Several econometric models can be derived from an economic model. Such models differ due to different choice of functional form, specification of stochastic structure of the v…

… (315 more words) …