1
Probability Distributions, Continuous
Variables
Objectives:
(Chapter 6, DeCoursey)
 To establish the difference between probability
distribution for discrete and continuous
distribution for discrete and continuous
variables.
 To learn how to calculate the probability that a
random variable, X, will fall between the limits
of “a” and “b”.
A continuous variable, X, can take on an infinite number
of values over a particular interval [a, b].
Probability Distributions, Continuous
Variables
f(x)
The probability that the variable X will lie between theses
two endpoints is given by
∫
=
≤
≤
b
a
dx
x
f
b
x
a
)
(
]
Pr[
([a, b] is subinterval.)
a
b
f(x)
≥
0, f(x) is called probability density function.
Probability Distributions, Continuous
Variables
a
b
f(x)
∫
=
≤
≤
b
a
dx
x
f
b
x
a
)
(
]
Pr[
([a, b] is subinterval.)
∑
≤
≤
b
x
a
i
i
x
p
)
(
Compared with discrete variable:
Cumulative Distribution:
The probability that the
continuous random variable is less than some upper
value, call it x
1
, is given by
∫
=
≤
1
)
(
]
Pr[
1
x
dx
x
f
x
X
Probability Distributions, Continuous
Variables
∞
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 Fall '11
 Glyn
 Math, Probability, Probability distribution, Probability theory, probability density function

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