A fair die with 4 sides is rolled 17 times. find the variance of the sum of the die rolls
2026-04-02 23:34:30.1775172870
How to find variance for the given problem?
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Recall that if $X,Y$ are independent, then $\text{Var}[X+Y]=\text{Var}[X]+ \text{Var}[Y]$. Indeed, this is because $\mathbb{E}[XY]=\mathbb{E}[X]\mathbb{E}[Y]$ and the cross terms vanish from the variance computation.
In particular, if $X_1,\ldots,X_n$ are $n$ i.i.d. die rolls, we have that $\text{Var}[X_1+\ldots+X_n]=n\text{Var}[X_1]=n (15/2 - 25/4) = 1.25n$