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5/15/10
The distribution of the amount of gravel (in tons) sold
by a construction company in a given week is a
continuous random variable,
X
, with pdf
given by:
Determine the mean/expected value, variance and
median for this distribution.
( 29
2
3
1
0
1
( )
2
0,
otherwise
x
x
f x

≤
≤
=
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Suppose
X
and
Y
are random variables with joint
probability distribution given by
f(x,y)
.
Marginal Distributions
( )
( , )
g x
f x y dy
∞
∞
=
∫
( )
( , )
h x
f x y dx
∞
∞
=
∫
5/15/10
Suppose
X
and
Y
are random variables with joint
probability distribution given by
f(x,y)
.
The mean, or
expected value, of the random variables
X
and
Y
are:
( )
( , )
,
( )
( , )
,
continuous case.
X
Y
E X
x f x y dydx
E Y
y f x y dxdy
μ
∞
∞
∞
∞
∞
∞
∞
∞
=
=
⋅
=
=
⋅
∫ ∫
∫ ∫
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View Full Document 5/15/10
Suppose
X
and
Y
are random variables with joint
continuous probability distribution given by
f(x,y)
.
The
mean, or expected value, of the random variables
X
and
Y
are:
( )
( , )
,
( )
( , )
,
continuous case.
X
Y
x
y
E X
f x y dydx
E Y
f x y dxdy
μ
∞
∞
∞
∞
∞
∞
∞
∞
⋅
⋅
=
=
=
=
∫
∫
∫
∫
( )
g x
( )
h y
5/15/10
Suppose
X
and
Y
are random variables with joint
continuous probability distribution given by
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This note was uploaded on 05/14/2010 for the course MATH 360 taught by Professor Wallace during the Spring '10 term at SUNY Geneseo.
 Spring '10
 Wallace
 Variance

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