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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, science, economics 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:
- 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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