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?
Multiplying probabilities is a way to calculate the likelihood of two independent events occurring together, while sum of the squares is a mathematical operation used to find the total of squared values. These two concepts are unrelated and serve different purposes.
Multiplying probabilities should be used when calculating the likelihood of two independent events happening together, such as flipping heads on a coin twice in a row. Sum of the squares should be used when finding the total of squared values, such as in statistical analysis or calculating energy in physics.
No, they cannot be used interchangeably. Multiplying probabilities and sum of the squares serve different purposes and have different calculations. Using one in place of the other can lead to incorrect results.
To calculate multiplying probabilities, multiply the probabilities of each event happening together. For example, if the probability of flipping heads on a coin is 1/2 and the probability of rolling a 6 on a die is 1/6, the probability of flipping heads and rolling a 6 is (1/2)*(1/6) = 1/12. To calculate sum of the squares, square each value and then add them together. For example, if we have the values 2, 3, and 4, the sum of the squares would be (2^2) + (3^2) + (4^2) = 4 + 9 + 16 = 29.
Multiplying probabilities is used in probability and statistics to calculate the likelihood of multiple events occurring together. This is important in fields such as genetics, where the probability of inheriting certain traits from both parents needs to be calculated. Sum of the squares is used in statistical analysis to find the total of squared values, which is used in various equations and models to understand and analyze data in fields such as physics, economics, and psychology.