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APPENDIX G
Characteristics of random variables
The mean (𝜇) is generally known as the average value of the data set. For use in reliability
index it is also called the expected value (E(x)) (US ACE, 2006). The mean or expected value
of x is used to represent the first moment in reliability analysis. It is represented by the
equation:
𝜇𝑥 = �
𝑥
𝑁
where 𝑥 is a data point and N is the number of data points.
The variance (𝑉𝑎𝑟[𝑥]) is a measurement of the spread between numbers in a data set. It is the
average squared difference of each number from its mean and is represented by:
𝑉𝑎𝑟[𝑥] = �
[(𝑥 − 𝜇𝑥 )2 ]
𝑁−1
The standard deviation (𝜎𝑥 ) is equal to the square root of the variance and it is a measure of
how much the data points differ from the mean.
𝜎𝑥 = �𝑉𝑎𝑟[𝑥]
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