. For three events A,B, and C show that P(A ∩ B | C) = P(A | B ∩ C)P(B | C). . The independent random variables X and Y have the following expectations: E(X) = 3, E(X2) = 12, E(Y ) = 5, and E(Y 2) =...

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For three events A,B, and C show that P(A ∩ B | C) = P(A |

B ∩ C)P(B | C).

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The independent random variables X and Y have the following

expectations: E(X) = 3, E(X2) = 12, E(Y ) = 5, and E(Y 2) = 30. Find

(a) E(X + Y ), E(2X + 1), E(2X + 0.3Y ) and E(2X − 0.3Y ).

(b) VarX, VarY, Var(2X +5), Var(X +Y ), Var(5X +7Y ), Var(5X −7Y ), and

Var(5X + 7Y + 1600).