Page 10 - DMTH404_STATISTICS

Statistics

Notes 1.1 Random Experiments

We give below some examples of a random experiment :
 A physicist performs an experiment to discover laws governing the flow of an electrical
current or the propagation of sound, heat or light etc.
 A chemist studies the reactions of chemicals and tries to understand the chemical properties
of matter.

 A physician compares two or more drugs to find out the most effective one by trying them
out on experimental animals or on patients.

 To describe the relationship between the price of a commodity and its demand and supply,
an economist observes the values assumed by these variables by conducting a market
survey over a period of time.

With a little imagination, we can construct many more examples of such experiments.
Experimentation is not necessarily restricted to a laboratory or to a university or a college. It
forms an important part of our everyday life. When you buy a dress or a shirt, when you vote for
a candidate at an electron, which you inspect a few grains of rice to decide whether the rice is
cooked or not, when you decide to register for this course, you are performing an experiment.
Thus, experimentation constitutes an integral part of our lives as well as our learning processes.
In this unit we shall develop methods of describing the results of an experiment. Once we can
describe the results we’ll be able io talk about the chances of their occurrence.
Consider the following simple experiments :
Experiment 1 : A stone is allowed to fall freely from height and we observe whether or not the
stone hits the ground.
Experiment 2 : Water in a pot is heated for a sufficiently long time to a temperature greater than
100°C. We observe whether the water turns into steam.
In these experiments, we have no doubt about the final outcome. The stone will eventually hit
the ground. The water in the pot will ultimately turn into steam. These experiments have only
one possible outcome. Even if these experiments are repeated again and again, every such
repetition will yield the same result.

On the other hand, in the following experiments there are two or more possible results.
Experiment 3 : A coin is tossed to deoide which of the two teams A and B would bat first in a
game of cricket. The coin may tum up a head or a tail.

Experiment 4 : A person coming out of a polling centre is requested to disclose the name of the
candidate in whose favour he/she has voted. Helshe may refuse to tell us or give the name of
any one of the candidate.
Experiment 5 : Three consecutive items produced by a machine are inspected and classified as
good or bad (defective). We may get 0, 1,2, or 3 defective items as a result of this inspection.

Experiment 6 : A newly invented vaccine against a disease is given to 30 healthy people. These
thirty people as well as another group of 20 similar people who are not vaccinated, are watched
over the next six months to see whether they develop the disease. The total number of affected
people may vary between 0 and 50.
Experiment 7 : A small town has 100 telephones. The number of busy telephones between 9 and
10 a.m. is noted for each day of a week. The number of busy telephones may be any number
between 0 to 100.

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