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Events and Sample Space

An observation (measurement) is the result of an experiment. It refers to the process of gathering and/or measuring data. This can be done by a physical or chemical experiment, but it also includes data from surveys or economic data (e.g. stock prices). The only requirement is that the outcome is not certain, i.e. not known in advance.

When we perform the experiment of throwing a die and recording the number on the top face, we have six possible outcomes of this experiment. For each experiment we can observe one and only one of these six basic outcomes and the outcome cannot be predicted with certainty. The outcome cannot be broken down into more basic outcomes. The collection (set) of all basic outcomes is called sample space. Since observing the outcome of an experiment is similar to selecting a sample from a population (in our case the sample space), the basic outcomes are called sample points.
 
Experiment An experiment is an act of observation that leads to a single outcome that cannot be predicted with certainty.
Sample Point A sample point is the most basic outcome of an experiment.
Sample Space The sample space of an experiment is the collection of all its sample points.
Event  An event is a specific collection of sample points.

 

Example:

What are the sample points of the experiment of tossing two coins and recording their up face?
It is important to note that we have to distinguish between the cases where coin 1 shows head and coin 2 tail and when coin 1 shows tail and coin 2 head, despite the fact that the coins appear to be identical. So we have four different possible outcomes (sample points) and our sample space is:
HH      HT      TH      TT

H ... head, T ... tail
A compounded event would be: throwing exactly one head, since it would consist of two sample points: HT and TH.

Last Update: 2006-Jšn-17