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Unformatted text preview: RVs
are statistically independent, the expectation for the multiple random variables
can be expressed as, 5. Covariance of Multiple RVs
As we know from previous lectures, covariance is a measure of joint variation. The
is defined as the expectation of the product
covariance of two random variables
between the respective deviations from their mean. This expectation in covariance is with respect to the joint distribution of
and and , we can get the covariance as, . So, for any
. If are statistically independent random variables, then we get,
and Here one should note always that converse is not true.
If and are any two random variables and and are any two constants, then . The variance of the sum of terms representing the variance of
each of the variables and a third term representing their covariance If and are independent random variables, then
. as So from the equation of covariance, the following facts to be noted: is large and positive when
tend to be both large, or both small,
with respect to their means.
If one variable is large and other tends to be small, the covariance is large and
If there is no relationship between the two variables, the covariance does not exist 6. Correlation of Multiple RVs
is a measure of the linear interrelationship between Thus, coefficient of linear correlation
and and . The is the normalized covariance between two variable...
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- Spring '13
- Civil Engineering