Statistical Uncertainty for Discrete Events

In summary, the conversation discusses the uncertainty in the number of times a specific total appears when two six-sided dice are rolled together N times. The method of finding this uncertainty involves using the binomial distribution and calculating the entropy of the distribution. This can be helpful in understanding the distribution of outcomes for a specific total, such as the number of times 8 appears when N is 100.
  • #1
gluons
15
0
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?
 
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  • #2
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.
 
  • #3
Thank you! The binomial test was just what I was looking for.
 

1. What is statistical uncertainty for discrete events?

Statistical uncertainty for discrete events refers to the variation or randomness in the outcomes of a discrete event or experiment. It is a measure of how confident we are in the results obtained from a sample of data and is often expressed as a range of possible values.

2. How is statistical uncertainty calculated?

Statistical uncertainty is calculated using statistical methods such as standard deviation, confidence intervals, and hypothesis testing. These methods take into account the sample size, variability of the data, and the level of confidence desired to estimate the uncertainty in the results.

3. Why is it important to consider statistical uncertainty?

Statistical uncertainty is important because it allows us to understand the reliability and validity of our results. It helps us to determine whether the differences observed in the data are due to chance or are actually significant. It also allows us to make informed decisions based on the level of uncertainty associated with the data.

4. How can statistical uncertainty be reduced?

Statistical uncertainty can be reduced by increasing the sample size, using more precise measurement techniques, and controlling for variables that may impact the results. Additionally, using more advanced statistical methods and conducting multiple trials can also help to reduce uncertainty.

5. How does statistical uncertainty differ from measurement error?

Statistical uncertainty and measurement error are closely related but differ in their sources. Measurement error refers to the differences between the true value of a measurement and the observed value due to limitations in the measurement process. On the other hand, statistical uncertainty is a measure of the variability in the data and takes into account both measurement error and other sources of variation.

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