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Unformatted text preview: tionship between two variables, it does not imply a casual effect
between the variables. For example, any two variables ( and ) may both depend on a third variable, in which case there will be a strong correlation between the values of and , but the values of one variable may not have direct effect on the values of the other one.
Problem 1. Life of structure, consist of two members, depends on their individual life time
as: , which are exponentially distributed. The joint density-function of Where mean of and . Determine the covariance between and and is given . Solution. We have, Therefore the covariance is: . The result of this numerical problem is no covariance between the two variables,
which are independent. Problem 2. The joint density of two random variables and and is given by: . Determine the covariance between and . Solution. In order to determine the covariance, first we have to compute the expected value of
and . So, expected value of Now expected value of And expected value of Then, the covariance of and can be calculated as,...
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- Spring '13
- Civil Engineering