1show that covxy exy - exey remember that gx ex and gy , Ask an Expert

Statistics

1. Show that Cov(XY) = E[XY] - E[X]E[Y]. Remember that gx = E[X] and gy = E[Y].

2. Prove that Var( X + Y) = Var X + Var Y + 2 Cov( X, Y).

3. Use the result of Exercise 25 to show that if A and Y are independent then Var( X + Y) = Var X + Var Y. This proves the third rule for variance.

Exercise 25

Prove that Var( X + Y) = Var X + Var Y + 2 Cov( X, Y).

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