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Determine whether E[X|X>2] + E[Y|X>2] can always be combined to form E[X+Y| X>2] or not. Give...

Determine whether E[X|X>2] + E[Y|X>2] can always be combined to form E[X+Y| X>2] or not. Give clear reasoning for full marks.

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Answer #1

Let Z = X + Y

Let Rx, Ry, Rz be the regions over which x, y, z are defined/

Given X > 2,  the conditional distribution of Z = X + Y will be different than the conditional distribution of X and Y,

Thus, E[X|X>2] + E[Y|X>2] cannot always be combined to form E[X+Y| X>2]

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