Chapter 1
Discrete Probability
Distributions
1.1
Simulation of Discrete Probabilities
Probability
In this chapter, we shall first consider chance experiments with a finite number of
possible outcomes
ω
1
,
ω
2
, . . . ,
ω
n
.
For example, we roll a die and the possible
outcomes are 1, 2, 3, 4, 5, 6 corresponding to the side that turns up. We toss a coin
with possible outcomes H (heads) and T (tails).
It is frequently useful to be able to refer to an outcome of an experiment. For
example, we might want to write the mathematical expression which gives the sum
of four rolls of a die. To do this, we could let
X
i
,
i
= 1
,
2
,
3
,
4
,
represent the values
of the outcomes of the four rolls, and then we could write the expression
X
1
+
X
2
+
X
3
+
X
4
for the sum of the four rolls. The
X
i
’s are called
random variables
. A random vari
able is simply an expression whose value is the outcome of a particular experiment.
Just as in the case of other types of variables in mathematics, random variables can
take on di
ff
erent values.
Let
X
be the random variable which represents the roll of one die.
We shall
assign probabilities to the possible outcomes of this experiment.
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 Spring '09
 scf
 Randomness, Discrete probability distribution, possible outcomes, Simulation of Discrete Probabilities

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