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Xaviers Institute of Business Management Studies

 

Quantitative Techniques

 

Please attempt any one question out of section A and any 10 questions out of Section B.

The section A is for 20 Marks and Section B is for 60 Marks (6 Marks X 10 Questions)

 

 

Total Marks – 80

Section A

 

Question. 1.       Distinguish between decision making under certainty and decision making under uncertainty. Mention certain methods for solving decision problems under uncertainty. Discuss how these methods can be applied to solve decision problems.

 

Question. 2.       Distinguish between probability and non-probability sampling. Elucidate the reasons for the use of non-probability sampling in many situations in spite of its theoretical weaknesses.

Answer: What is non-probability sampling?

Non-probability sampling (sometimes nonprobability sampling) is a branch of sample selection that uses non-random ways to select a group of people to participate in research.

Unlike probability sampling and its methods, non-probability sampling doesn’t focus on accurately representing all members of a large population within a smaller sample group of participants. As a result, not all members of the

 

Question. 3.       What are models? Discuss the role of models in decision-making. How can you classify models on the basis of behavior characteristics?

Question. 4.       What are matrices? How are determinants different from matrices? Discuss few applications of matrices in business.

 

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Section B

 

Write short notes on any ten of the following:

(a) Concept of Maxima and Minima

 

(b) Types of classification of data

 

Answer:  Classification of data

The method of arranging data into homogeneous classes according to the common features present in the data is known as classification.

 

A planned data analysis system makes the fundamental data easy to find and recover. This can be of particular interest for legal discovery, risk management, and compliance. Written methods and sets of guidelines for data

 

 

 

 

(c) Pascal Distribution

(d) Multi-stage sampling & Multi-phase sampling

 

(e) Box-Jenkins Models for Time Series

Answer: Box-Jenkins  Methodology  and  autoregressive  integrated  moving-average  (ARIMA)  are synonymous  models  applied  to  time  series  analysis  and  forecasting.  The  methodology  for identifying,  fitting  and  checking  appropriate  ARIMA  model  studied  extensively  by  Box  and Jenkins(1976).  For this reason, ARIMA models of forecasting often  referred to  as Box-Jenkins Methodology. ARIMA models are a class of linear models that capable of representing stationary (without trend) and nonstationary (with trend) time series. The basis of the Box-Jenkins approach for  modelling

 

 

 

 (f) Determinant of a Square Matrix

Answer: The determinant of a matrix is a number that is specially defined only for square matrices. Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. Determinants also have wide applications in engineering, scienceeconomics and social science as well. Let’s now study about the determinant of a matrix.

 

 

 

(g) Primary and Secondary Data

Answer: What is Primary Data?

Primary data is the kind of data that is collected directly from the data source without going through any existing sources. It is mostly collected specially for a research project and may be shared publicly to be

 

 

 

(h) Bernoulli Process

 

Answer: Bernoulli process: A sequence of Bernoulli trials is called a Bernoulli process. Among other conclusions that could be reached, for n trials, the probability of n successes is pⁿ.

 

Bernoulli trial: A Bernoulli trial is an instantiation of a Bernoulli event. It is one of the simplest experiments that can be conducted in probability and statistics. It’s an experiment where there are two possible outcomes (Success and Failure).

The Bernoulli

 

 

 

(i) The Student’s t Distribution

Answer: The T distribution (also called Student’s T Distribution) is a family of distributions that look almost identical to the normal distribution curve, only a bit shorter and fatter. The t distribution is used instead of the normal distribution when you have small samples (for more on this, see: t-score vs. z

 

 

(j) Use of Auto-correlations in identifying Time Series

Answer: A time series, as the name suggests, is a series of data points that are listed in chronological order. More often than not, time series are used to track the changes of certain things over short and long periods — with the price of stocks or even other commodities being a prime example. Regardless, you’re taking a closer look at how something changes at regular intervals over time — which is important when attempting to use the past to forecast the future.

What is

 

 

 

 

 (K) Absolute value function

 

 (l) Quantiles

Answer: The word “quantile” comes from the word quantity. In simple terms, a quantile is where a sample is divided into equal-sized, adjacent, subgroups (that’s why it’s sometimes called a “fractile“). It can also refer to dividing a probability distribution into areas of equal probability.

The median is a quantile;

 

 

 (m) Criteria of pessimism in decision theory

“A decision  is the is a conclusion  of a process by which one choices between two or more available  courses of  action for the purpose of  attaining a goal”

  • A  decision an act of choice where in a manager forms a conclusion about what must be done under a given situation. And  decision making is a process to arrive at a decision , The process by witch an

 

 

 

(n) Cluster vs. Stratum

Answer: Differences Between Stratified and Cluster Sampling

The differences between stratified and cluster sampling can be drawn clearly on the following grounds:

  1. A probability sampling procedure in which the population is separated into different homogeneous segments called ‘strata’, and then the sample is chosen from the each stratum randomly, is

 

 

 (o) Moving average models

 

 (p) Step function

 

 (q) More than type ogive

 

 (r) Subjectivist’s criterion in decision making

 

 

(s) Double sampling

Answer: Double sampling is a two-phase method of sampling for an experiment, research project, or inspection. An initial sampling run is followed by preliminary analysis, after which another sample is taken and more analysis is run.

It is used in

 

 

 

 (t) Auto regressive models

 

 

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