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3
Random Variables,
Distributions, Moments,
and Statistics
3.1 RANDOM VARIABLES
We can dene a random variable (RV) once we have dened the sample space, based on the possible
events and their probabilities. An RV is a rule, or a function, or a map associating a number to each
event in the sample space (see Figure 3.1).
Example: In the roll of six-sided die, the events are A
i
= side facing up is i where i = 1, 2, …,
6 with P[A
i
] = 1/6. We can make a “discrete” RV, denoted by X, associating each event with
the value of the RV; for example, X taking values X = {1, 2, 3, 4, 5, 6} each with P[x
i
] = 1/6.
We refer to the type of RV described in the ...