Essay A1 Scenario You are working as a research technician at national research laboratory where good analytical skills and understanding of mathematics and Statistical analysis are essential for...

1
Essay 1

Scenario

You are working as a research technician at national research laboratory where
good analytical skills and understanding of mathematics and Statistical analysis
are essential for everyday work within your research group. Your line manager
has informed you that to have a successful promotion within your research
team during the forthcoming year you need improve and update your present
mathematical and Statistical skills so that you can deal with a variety of
problems where use of alge
aic, trigonometric equations and differentiation
and integration on variety of engineering, scientific analysis and calculations
are all essential for the new position. In addition, your line manager has also
highlighted the importance sound understanding of statistical data collection
and analysis that are required to enable you to make positive contributions to
your research team in particular with collection, and analysis of the data.
As preparatory task for your forthcoming promotion, your line manager has
presented with variety of mathematical and statistical problems and requested
from you to present your model solutions to his attention within 2 months to
enable him to consider your promotion within the company.

“Mathematical knowledge in theory and use of that very knowledge in real world
problems requires that one doesn’t have good knowledge only but also has
good co
elation abilities so that one can map real world problems with those
accounted in maths books. As for working in national research laboratory team it
is indispensable to know various analyzing tools I will try to learn as many
tools as I could, but not at the cost of quality of education. I will also try to
take up small projects related to mathematical and statistical problems, apart
from those assigned to me by the manager as it will not only let me to
develop better understanding of the subjects but also would be added to my
esume that would play a crucial role while being considered for promotion.

While preparing solution to the problems assigned by the manager I will try to
mention the various sources under references to explicitly make him know that I
have done a thorough literature survey to learn skills.”
2


1 a Explain Systematic E
ors and Random E
ors with suitable a case study for
each e
or. Briefly comment on your answer based on your explanation.

Ans:

E
ors in measurement systems or in any system(s) are highly undesirable as
it may even cause impediment in the normal operation of the system and
causes an e
oneous output. E
ors may arise from different sources and are
usually classified as under:

1. Systematic E
ors
2. Random E
ors
3. Gross E
ors

1. Systematic E
ors:

Systematic e
ors as the name itself implies arise due to either shortcomings
of the system eor due to ambient environment or both. Systematic e
or is
further classified as under
a. Instrumental E
ors
. Environmental E
ors
c. Observational E
ors
d.
Instrumental e
ors may arise due to
o Inherent shortcomings of the instrument
o Misuse of the instrument
o Loading effects of instruments

Inherent shortcomings e
ors are inherent in instruments because of their
(instruments’) mechanical structure. For example, if the spring (used for
producing control torque) of permanent magnet instrument has become
weak, the instrument will always read high. E
ors may be caused by
friction, hysteresis or even gear backlash.
Misuse of the instrument will of course
produce e
oneous results. For example, because of failure to adjust the
zero of instruments, poor initial adjustments, using leads to a high
esistance are few causes that may lead to an inaccurate result.
Loading effects has also been a
source of e
ors. For example, a well cali
ated voltmeter may give a
misleading reading when connected across a high resistance circuit.

Environmental e
ors arise due to the conditions external to the measuring
device including conditions in the area su
ounding the instrument. These
may be effects of temperature, pressure, humidity, etc.

Observational e
ors arise from various sources e.g. carelessly taken
eading, difference between any two persons while recording timing of the
event.
To better illustrate this let us discuss about the observational e
or on
account of PARALLAX- as in a analog voltmeter pointer rest slightly above
LO1: Task 1 (PASS)

3
the surface of the scale in order to avoid any e
or due to parallax it is
necessary that line of vision of the observer is exactly above the pointer. To
minimize e
or on account of parallax highly accurate meters are provided
with mi
ored scales.

Comments:

While making precise measurements we must recognize possibility of e
ors
or to at least reduce them to least possible extent. Few steps are mentioned
elow:
1. Procedure of measurement must be carefully planned;
substitution or cali
ation methods against standards may
e used.
2. After determining the instrumental e
ors; co
ection factor
should be applied.
3. It is necessary to ensure that operator has acquired
sufficient and necessary expertise to operate the
instruments.
Techniques that eliminate the effect of environmental distu
ance should be
applied e.g.-hermetically sealing the instrument make it


1 b A computer engineer created a program in which the input signals are
accepted from the sensors in the form of denary numbers and the output
device requires the signal to be in binary form, but the processor works
only based on the signals in the form of octal number. If the input is given
to be 5613.90625, then what will be the binary number for the output
signal? Give a
ief comment based on your answer.

Ans First we convert the given number in its equivalent binary representation.

Considering Integer Part

5613
2 2806 1
2 1403 0
2 701 1
2 350 0
2 175 0
2 87 1
2 43 1
2 21 1
2 10 1
2 5 0
2 2 1
2 1 0
...