Let X and Y be discrete random variables with joint probability mass function Pxy (x, y). Answer the following questions. a) Show that E[aX+bY+c]=aE[X]+bE[Y]+c, where a, b and c are scalar constants. b) Assume that X and Y are independent. Show that_E[XY]=E[X]E[Y]. c) Assume that X and Y are independent. Show that var (X+Y)= var(X)+ var (Y).

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