SUM OR DIFFERENCE OF TWO RANDOM VARIABLES: X1 AND X2


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

start example

Problem: Number of people in car pool

Experiment: Observe 20 consecutive cars in "HOV" lane

Assumption: Population is infinite

Find: Central tendencies and dispersions

click to expand

Mean of observed data: (use sub i for individual sample)

You should not expect the mean to equal an observable value, e.g., 3.

end example
 



Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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