# Throw a dice-expected value.

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.

• Can you compute the expectation of $X_i$? For $Y$ you can use linearity of expectation, which does not need independence. – Ross Millikan Jan 20 at 23:25
• 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). – Peter Foreman Jan 20 at 23:30
• @RossMillikan Yes, of course. You're right. – pawelK Jan 20 at 23:36