# ISS (Statistical Services) Statistics Paper III: Questions 94 - 104 of 109

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## Question number: 94

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

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Essay Question▾

### Describe in Detail

If Xn is a branching process with

and σ2= Var (X1), then show that

1. E (Xn) =mn

### Explanation

Let X0=1. It is evident

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

(i)

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## Question number: 95

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

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### Write in Short

What is Gambler’s ruin problem? Obtain the probability of ruin, if Gambler plays with a capital of a rupees.

## Question number: 96

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

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Essay Question▾

### Describe in Detail

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

(i) Pn (s) = Pn-1 [P (s) ]

(ii) ) Pn (s) = P [Pn-1 (s) ]

### Explanation

Consider a population consisting of individual, able to produce identical offsprings of the same type and dies after producing. Let Zij be the number of offspring produced by the jth individual of the ith generation and Xn be number of individual of the nth generation, j = 1,2, …, Xi and i = 0,1, 2, …

Let X0=1. It is evident

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## Question number: 97

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Essay Question▾

### Describe in Detail

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

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## Question number: 98

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Essay Question▾

### Describe in Detail

Explain meaning of econometric models.

### 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

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## Question number: 99

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### Write in Short

What is National Income?

## Question number: 100

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Essay Question▾

### Describe in Detail

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

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## Question number: 101

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### Describe in Detail

State and explain how to estimate Lorenz Curve.

### Explanation

Let X be the outcome variable of interest (e. g. income). The cumulative distribution function of X is given as and the quantile function (the inverse of the distribution function) is given as w

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## Question number: 102

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### Write in Short

What do you mean by econometrics?

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