Let X and Y be jointly distributed random variables with finite variances (a) Show that V a bX cY b 2 2 x c 2 2 Y 2bc XY (b) Use the above result to derive the variances of X Y and X Y (c) What happens to your results in (a) and (b) when X and Y are uncorrelated

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Question: Let X and Y be jointly distributed random variables with finite variances. (a) Show that V[a + bX + cY ] = b 2 2

Let X and Y be jointly distributed random variables with finite variances. (a) Show that V[a + bX + cY ] = b²²_x+ c²²_Y + 2bc_XY. (b) Use the above result to derive the variances of X + Y and X Y. (c) What happens to your results in (a) and (b) when X and Y are uncorrelated?

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