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Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
The expectation is given by
µ
Y
=
3a
1
+4a
2
a
1
+2a
2
yf
Y
(y) dy
=
a
1
+4a
2
a
1
+2a
2
y
1
4
y a
1
2a
2
a
1
a
2
dy +
3a
1
+2a
2
a
1
+4a
2
y
1
2a
1
dy
+
3a
1
+4a
2
3a
1
+2a
2
y
1
4
4a
2
+ y 3a
1
a
1
a
2
dy
= 2a
1
+ 3a
2
.
The same procedure can be used for the other three cases to show that the expectation is always 2a
1
+ 3a
2
.
111
4.20. Reconsider Example 4.8, supposing that the angles are random variables. The 30
angle now is a
random variable with mean of 30
and variance of 3
and the 45
angle now is a random variable with
mean of 45
and variance of 4
. The applied force has the same statistics as in the example. ...
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Publisher Resources

ISBN: 9781439849897