Six Sigma and Beyond: Statistics and Probability, Volume III
SUM OR DIFFERENCE OF TWO RANDOM VARIABLES: X 1 AND X 2
Y = a 1 X 1 ± a 2 X 2
Mean: ¼ Y = a 1 ¼ X1 ± a 2 ¼ X2
Variances: ƒ 2 Y = a 1 2 ƒ 2 X1 + a 2 2 ƒ 2 X2 ± a 1 a 2 ƒ 2 X1X2
Where Covariance: ƒ 2 X1X2 = 0, if independent
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Problem: Number of people in car pool
Experiment: Observe 20 consecutive cars in "HOV" lane
Assumption: Population is infinite
Find: Central tendencies and dispersions
Mean of observed data: (use sub i for individual sample)
You should not expect the mean to equal an observable value, e.g., 3.
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