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We throw the dice three times. Let $X_i$- number of throws, in which we get number $i$. Find expected value and variance random variable $Y=\sum_{i=1}^{6} (-1)^iX_i$. We know, that $X_i=0,1,2,3$. $E(Y)=E(-X_1+X_2-X_3+X_4-X_5+X_6)$. But $X_i$ are not independent. And I don't know what to do next.

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    $\begingroup$ Can you compute the expectation of $X_i$? For $Y$ you can use linearity of expectation, which does not need independence. $\endgroup$ – Ross Millikan Jan 20 at 23:25
  • $\begingroup$ The expected value of $Y$ is just zero as all of $X_i$ should have the same value (all sides of the die have equal chances of being rolled). $\endgroup$ – Peter Foreman Jan 20 at 23:30
  • $\begingroup$ @RossMillikan Yes, of course. You're right. $\endgroup$ – pawelK Jan 20 at 23:36

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