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The random variables X and Y are independent. The expected value of X is 1 and that of Y is 2. The variance of X

The random variables X and Y are independent. The expected value of X is 1 and that of Y is 2. The variance of X is 3 and that of Y is 5, respectively.

What is:

  1. E(X + Y)
  2. E(X - Y)
  3. E(2X - Y + 1)
  4. E(3XY + 2)
  5. Var(X + Y)
  6. Var(X - Y)
  7. Var(2X - Y +1)
  8. Var(3XY + 2)

How would the results change, if X and Y correlated so, that Cov(X,Y) = -2 ?

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