Let X and Y be an arbitrary integrable random variables on (N, F, P), and let Z(w) = aX(w) + bY (w), where a, b e R. Prove formally, from first princi- ples (starting with simple functions, then non-negative, then arbitrary) the linearity

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Let X and Y be an arbitrary integrable random variables on (2, F, P),
aX(w) + bY (w), where a, b E R. Prove formally, from first princi-
ples (starting with simple functions, then non-negative, then arbitrary) the linearity
and let Z(w)
property that E[Z(w)] = aE[X(w)] +bE[Y (w)].
Transcribed Image Text:Let X and Y be an arbitrary integrable random variables on (2, F, P), aX(w) + bY (w), where a, b E R. Prove formally, from first princi- ples (starting with simple functions, then non-negative, then arbitrary) the linearity and let Z(w) property that E[Z(w)] = aE[X(w)] +bE[Y (w)].
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