I want to find the expected value and variance of the total spots from 60 fair die rolls.
The way I tried approaching this is we know that (if x = total value of all die rolls) that $P(x = 60) = (1/6)^{60}$ and $P(x=360) = (1/6)^{60}$ and then calculating $E(x) = 60*(1/6)^{60} + 360(1/6)^{60}$ which obviously comes up with a very small fraction.
How would one approach this problem? Thanks in advance for the help!
If the rolls of the dice are independent, then you can solve the problem by finding the expected value and variance of a single roll, then multiplying by 60. (In fact, the independence is only needed for the variances to add.)