What is a Statistical Experiment?
All statistical experiments have three things in common:
-
The outcome of the experiment depends on chance.
A coin toss has all the attributes of a statistical experiment. There is more
than one possible outcome. We can specify each possible outcome (i.e., heads or
tails) in advance. And there is an element of chance, since the outcome is
uncertain.
The Sample Space
-
An event is a subset of a sample space - one or more sample
points.
Probability of an Event
With some statistical experiments, each sample point is equally likely to occur. In this situation, the probability of an event is very easy to compute.
It is:
P(E) = |
Number of sample points in event |
Number of sample points in sample space |
|
Think about the toss of a single die. The sample space consists
of six possible outcomes (1, 2, 3, 4, 5, and 6). And each outcome is equally likely to occur. Suppose we defined
Event A to be the die landing on an odd number. There are three odd numbers (1, 3, and 5). So, the probability
of Event A would be 3/6 or 0.5.
Types of events
-
Two events are independent when the occurrence of one does not
affect the probability of the occurrence of the other.