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# What is a Random Experiment?

Module by: Christopher Chikalimba-Gama. E-mail the author

Summary: This module defines a Ramdom Experiment and some of its examples.

A Random Experiment is an experiment, trial, or observation that can be repeated numerous times under the same conditions. The outcome of an individual random experiment must be independent and identically distributed. It must in no way be affected by any previous outcome and cannot be predicted with certainty.

## Examples of a Random experiment include:

• The tossing of a coin. The experiment can yield two possible outcomes, heads or tails.
• The roll of a die. The experiment can yield six possible outcomes, this outcome is the number 1 to 6 as the die faces are labelled
• The selection of a numbered ball (1-50) in an urn. The experiment can yield 50 possible outcomes.
• Percentage of calls dropped due to errors over a particular time period. The experiment can yield several different outcomes in the region 0 - 100%.
• The time difference between two messages arriving at a message centre. This experiment can yield any number of possible outcomes.
• The time difference between two different voice calls over a particular network. This too can yield any number of possible outcomes.

## Exercise 1

Is the lotto draw considered as a random experiment?

### Solution

No. The lotto draw is not a random experiment. This is because it cannot be repeated under the same conditions. The conditions are different because as a lotto ball is selected, it remains outside the urn. This decreases the number of balls inside the urn, thus changing the experiment.

## Exercise 2

Can an observation over "pure-chance traffic " in Teletraffic be considered a random experiment?

### Solution

Yes. It is considered a random experiment because call arrivals and terminations are independent, identically distributed, random events. They are in no way affected by any previous calls made. Although a particular customer does not make calls at random, the traffic generated by a large number of customers can, however, be seen to be random traffic.

## Reference

1. Ali M. Probalistic system analyses: Part I. University of the witwatersrand, 2000.
2. Dr Ian Kennedy. Teletraffic Engineering Lecture Notes: Teletraffic Theory. University of the witwatersrand, 2006. Http://dept.ee.wits.ac.za/~kennedy/elen5007/ coursepack/course/prchnctr.htm (last accessed 25 February 2006).

Co-Author: Brandon Hodgson

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