The discussion clarifies the distinction between multiplying probabilities and using the sum of the squares in the context of uncorrelated probabilistic events. When calculating the probability of two independent events both occurring beyond a certain threshold, such as 3.3 sigma, the correct approach is to multiply the probabilities (e.g., 0.001 * 0.001). The sum of the squares is not applicable for probabilities but is relevant when calculating the variance of the sum of two random variables, where the standard deviations are squared and summed.
PREREQUISITESStatisticians, data analysts, and anyone involved in probability theory or statistical modeling who seeks to understand the nuances of calculating probabilities for independent and uncorrelated events.
Uncorrelated and independent are different things. If they are independent then you multiply the probabilities. Correlation is simply one specific type of dependence. However, it is easy to come up with examples where one event causes the other with 100% certainty (so the probability of seeing them both is equal to the probability of the cause) and yet they are uncorrelated.jaydnul said:If I have two uncorrelated probabilistic events, and I want to know the probability of seeing them both land beyond 3.3 sigma (for example), do I multiply the probabilities .001*.001 or do I do sum of the squares sqrt(.001^2 + .001^2).
I don't know of a context where you use the sum of the squares of the probabilities. That could easily lead to a number greater than 1, which couldn’t be a probability.jaydnul said:explain what context we would use sum of the squares instead?