Variance of rolls needed for rolling a 6

Question

I have an random variable that counts the number of dice rolled until I rolled a 6. Let's call it $X$.

I understand that $E[X] = {1\over 6} \sum n({5\over 6})^n = 5$

I wonder, though, how to find the variance of such $X$.

Answer 1

Try using $Var[X] = E[X^2] - E[X]^2.$

You're equation will alter slightly for $E[X^2]$ and then subtract the square of your previous answer.