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"Suppose two six-sided dice are rolled together N times. What is the uncertainty in the number of times any given total appears on the dice?"

For example, what is the uncertainty in the number of times 8 is rolled if N is 100? (You can call the number of times 8 appears another variable such as m).

I can see how you would analyze this system by finding the mean and variance of the distribution, but what if I just want to know the uncertainty in only

*one*channel of the distribution?