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Math · Statistics And Probability
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Linearity of Expectation operator If If X1,X2,,Xk are random variables and a, az,.ak are constants, then the expectation of of the random variable y ajX, is given by i-1 i= 1 Proof. The demanding part is showing that E(X1 + X2-E (X) + E(X2). Letting Z = X + Y, the convolution formula yields E(Z) = E(X + Y) = | zf2(2)dz = | z | fx.y@-у, у)dydz =1 [I zTxy@-y, y)dzldy

(Rigorous) Proof of the linearity of an expectation operator. I need help understanding the step from the first line to the second of the proof - namely how has the z shifted into integral next to the joint density of f_{X,Y} and how have the respects of integration changed order.

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