r4_randomvar - 13.42 Design Principles for Ocean Vehicles...

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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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13.42 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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r4_randomvar - 13.42 Design Principles for Ocean Vehicles...

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