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mathstrike
mathstrike
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We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. If we assume that E(X+Y) exists, couldCould we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)

We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. If we assume that E(X+Y) exists, could we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)

We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. Could we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)

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mathstrike
mathstrike
  • 1
  • 2

We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. If we assume that E(X+Y) exists, could we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)

We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. could we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)

We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. If we assume that E(X+Y) exists, could we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)

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mathstrike
mathstrike
  • 1
  • 2

Expectation where linearity does not hold

We have four random variables say W,X,Y,Z where W and X has the same distribution and Y, Z also has the same distribution. Bad news is EX and EY may not exist but E(W+Z) is zero. could we conclude that E(X+Y) is zero? ( I know if EX and EY where defined we used linearity and it is obvious, also we know nothing more about X, Y)