Statistical Methods for Quality Assurance by Stephen B. Vardeman & J. Marcus Jobe

Author:Stephen B. Vardeman & J. Marcus Jobe
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Mean of a Linear Function of k Random Variables

Variance of a Linear Function of k Independent Random Variables

For the very simplest of functions g relating system inputs to the output U, it is possible to provide expressions for the mean and variance of U in terms of the means and variances of the inputs. Consider the case where g is linear in the inputs, that is, for constants a 0, a 1, …, a k , suppose that

(4.22)

Then if the variables X, Y, …, Z are independent with respective means μ X , μ Y , …, μ Z and variances σ X 2, σ Y  2, …, σ Z 2, U has mean

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