I'll post my work, but I'm not sure how to calculate variance. The question asks for the expected sum of 3 dice rolls and the variance. I think I got the expected sum.
Any help would be awesome 🙂 thanks!
[Math] How to calculate variance for sum of dice
combinatoricsdiscrete mathematicsprobability
Best Answer
The variance calculation is incorrect. Let random variables $X_1,X_2,X_3$ denote the results on the first roll, the second, and the third. The $X_i$ are independent. The variance of a sum of independent random variables is the sum of the variances. Since the variance of each roll is the same, and there are three die rolls, our desired variance is $3\operatorname{Var}(X_1)$.
To calculate the variance of $X_1$, we calculate $E(X_1^2)-(E(X_1))^2$. And $$E(X_1^2)=\frac{1}{6}\left(1^2+2^2+\cdots+6^2\right).$$