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13.42 Design Principles for Ocean Vehicles
Reading #
13.42 Design Principles for Ocean Vehicles
Prof. A.H. Techet
Spring 2005
1. Random Variables
A random variable is a variable,
x
, whose value is assigned through a rule and a random
experiment,
ζ
, that assigns a priori a value to the outcome of each experiment,
AA
2
,
A
,...
This rule states that
1
,
3
x
()
A
=
x
1
1
x
A
=
x
2
2
L
=
x
x A
n
n
One example of a random variable is a Bernoulli random variable which assigns either a
1 or 0 to the outcome. For example, toss a “fair” coin. If it lands heads up you get one
dollar, if it land tails up you loose a dollar. The amount won or lost in this case is the
random variable.
Symbolically,
x
denotes the random variable which is a “function” of the random
event
=
{
AA
,
…
A
n
} which has associated probabilities:
p
A
=
p
,
p
A
=
p
, etc.
1
,
2
,
1
1
2
2
A
⎯→
x
,
p
1
1
1
A
2
⎯→
x
2
,
p
2
M
A
⎯→
x
,
p
n
n
n
©2004, 2005
A. H. Techet
1
Version 3.1, updated 2/14/2005
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View Full Document13.42 Design Principles for Ocean Vehicles
Reading #
The variables
x
i
are the values of the random variable,
A
, the possible events in the
i
event space, and
p
i
is the probability of event
A
i
.
EXPECTED VALUE
of the random variable can be thought of as follows: after many
(
M
) repetitions of a random experiment in which event
A
1
occurred
d
1
times,
A
2
occurred
d
2
times, and so on to
A
occurred
d
times, the total number of experiments is
n
n
simply
M
=
d
1
+
d
+
d
3
+
L
+
d
.
(19)
2
n
If a weight, or cost,
x
i
, is assigned to each event,
A
, then the total cost of all of the
i
events is
x
T
=
dx
+
d
x
2
+
L
+
.
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 Spring '05
 AlexandraTechet

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