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
Describe in Detail
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)
… (83 more words) …
Question number: 95
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
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
Describe in Detail
Define a Galton Watson branching process. If {p_{k}} is the offspring distribution, then prove the following identities:
(i) P_{n} (s) = P_{n1} [P (s) ]
(ii) ) P_{n} (s) = P [P_{n1} (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
… (114 more words) …
Question number: 97
» Econometrics » Instrumental Variable Estimation
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
… (187 more words) …
Question number: 98
» Econometrics » General Linear Model (GLM)
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
… (153 more words) …
Question number: 99
» Econometrics » Nature of Econometrics
Write in Short
What is National Income?
Question number: 100
» Econometrics » Nature of Econometrics
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
… (317 more words) …
Question number: 101
» Econometrics » Nature of Econometrics
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
» Econometrics » Nature of Econometrics
Write in Short
What do you mean by econometrics?
Question number: 103
» Econometrics » Nature of Econometrics
Write in Short
State and explain estimating Concentration Curve.
Question number: 104
» Econometrics » Nature of Econometrics
Write in Short
Describe estimation of Demand Function.