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Chapter 12
Continuous Random Variables
and their Probability Distributions
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View Full Document Probability Distributions of a
Continuous Random Variable
For a continuous random variable X, a probability density
function such that
•
•
•
•
0
)
(
≥
x
f
∫
∞
∞

=
1
)
(
dx
x
f
b
to
a
from
x
f
under
area
dx
x
f
b
x
a
P
b
a
)
(
)
(
)
(
=
=
≤
≤
∫
0
)
(
=
=
x
X
P
Probability Distributions of a
Continuous Random Variable
For a continuous random variable X, a probability cumulative
function:
•
∫
∞

=
≤
=
x
du
u
f
x
X
P
x
F
)
(
)
(
)
(
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View Full Document Mean & Standard Deviation of a
Continuous Random Variable
2
2
2
2
)
(
)
(
)
(
)
(
μ
σ

=

=
=
∫
∫
∞
∞

∞
∞

dx
x
f
x
dx
x
f
x
X
V
2
σ=
∫
∞
∞

=
=
dx
x
xf
X
E
)
(
)
(
Continuous Probability
Distributions
•
Continuous Uniform Distribution
•
Normal Distribution
•
Exponential Distribution
•
Erlang and Gamma Distributions
•
Weibull Distribution
•
Lognormal Distribution
•
Beta Distribution
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View Full Document
•
Probability Density Function
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This note was uploaded on 12/03/2011 for the course EIN 5226 taught by Professor Staff during the Fall '11 term at FIU.
 Fall '11
 STAFF

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