Statistical Uncertainty for Discrete Events

[gluons]

I am not sure how to answer the following question, which I have posed to myself to better understand the method:

"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?

 

[mXSCNT]

Well, the first step is to find the distribution for that specific total. For that you can use the binomial distribution, where in your example p = the probability that 8 comes up on a single roll. You then just need to use the entropy of the binomial distribution.

 

[gluons]

Thank you! The binomial test was just what I was looking for.