Random Variable
A random variable is a function defined on the Probability Space .
Random Variables are distinguished between discrete and continuous ones. Random Variables can have an Expected Value and a Variance .
Example (discrete) Experiment #
-
where 
is the Powerset
of 
-
We can now coose a random variable 
to be the number that appears on the
die (this is allowed since the numbers on the die are also in 
)
We could choose it differently if we wanted, but this is what we got:
.
Since the subset of that maps to is discret, is a
discrete random variable.
Then:
Example (continuous) Experiment #
Setting: Radioactive decay
We chose 
the time it takes for a radioactive particle to
decay. Since 
is continuous, the random variable is also continuous.
