Section 2.4: Random Variables
Random Variable
•
a mapping from the sample space to the real line
→
It assigns a numerical value to each outcome in a sample space.
•
It is customary to denote random variables with capital letters:
X
,
Y
etc.
•
Use lowercase letters,
x
,
y
etc., to denote the values of random variables take.
e.g.) For a toss of a coin,
S
=
{
H,T
}
. Let
X
=
0
if head(H) comes up
1
it tail(T) comes up
X
is a random variable.
Types of Random Variables
•
Discrete
: can take only a countable number of distinct values
e.g.) # of children in a family, the population size of a city, # of cars passing an
intersection in a min
•
Continuous
: takes on values on a continuous interval
e.g.) height, diameter of a disc, the amount of electricity used in a month
Probability Distributions for Discrete Random Variable
The
probability distribution
(pd) or
probability mass function
(pmf) of a discrete random
variable
X
is given the function
p
(
x
) =
P
(
X
=
x
).
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 Spring '08
 Kyung
 Statistics, #, CDF, discrete random variable

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