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Chapter 2 – Linear Combinations of Random Variables
When students have completed this lesson they should be able to:
- E(aX + b) = aE(X) + b and Var(aX + b) = a^2Var(X)
- E(aX + bY) = aE(X) + bE(Y)
- Var(aX + bY) = a^2Var(X) + b^2Var(Y) for independent X and Y
- If X has a normal distribution, then so does aX + b
- Is X and Y have independent normal distributions, then aX + bY has a normal distribution
- If X and Y have independent Poisson distributions, the X + Y has a Poisson distribution