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Combining Random Variables

Combining Random Variables. lecture chapter 16 part 2. The rules!. E(X ± c) = E(X) ± c E( aX ) = a E(X) Var (X ± c) = Var (X) Var ( aX ) = a 2 Var (X). E(X ± Y) = E(X) ± E(Y) Var (X ± Y) = Var (X) + Var (Y) (X & Y must be independent) {the pythagorean Theorem of Stats) .

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Combining Random Variables

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  1. Combining Random Variables lecture chapter 16 part 2

  2. The rules! E(X ± c) = E(X) ± c E(aX) = a E(X) Var(X ± c) = Var(X) Var(aX) = a2Var(X) E(X ± Y) = E(X) ± E(Y) Var(X ± Y) = Var(X) + Var(Y) (X & Y must be independent) {the pythagorean Theorem of Stats)

  3. A grocery supplier believes that in a dozen eggs the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy 3 dozen eggs without checking them! (living dangerously) 1) How many broken eggs do you expect to get? 2) What’s the standard deviation? 3) what assumptions did you have to make about the eggs?

  4. The American Vet Association claims that the annual cost of medical care for dogs averages $100 with a stddev of $30 and for cats averages $120, with a stddev of $35. 1) What’s the expected difference in cost for care for dogs & cats? 2) What’s the standard deviation of the difference? 3) If the costs can be described by a normal model, what’s the probability that medial expenses are higher for someone’s dog than for their cat? 4) What concerns do you have?

  5. In the 4 X 100 medley relay, 4 swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times of their swimmers and creates a model assuming that the swimmers performances are independent and follow a normal model. 1) What are the mean and stddev for the relay teams’s total time? 2) The team’s best time so far this season was 3:19.48 or 199.48 seconds. Do you think the team is likely to swim faster than this at the conference championship? Explain.

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