1

I often hear people talk about correlation between events, e.g. event A and event B are positively correlated.

However, unlike correlation between random variables (i.e. $\frac{Cov(X,Y)}{\sigma_X \sigma_Y}$ ), I can't seem to find a numeric definition of correlation between events.

In this book, it is mentioned that

  1. $\mathbb{P}(∣)$ > $\mathbb{P}()$ if and only if $\mathbb{P}(∣)$ > $\mathbb{P}()$ if and only if $\mathbb{P}(∩) > \mathbb{P}()\mathbb{P}()$. In this case, and are positively correlated.
  2. $\mathbb{P}(∣) < \mathbb{P}()$ if and only if $\mathbb{P}(∣) < \mathbb{P}()$ if and only if $\mathbb{P}(∩) < \mathbb{P}()\mathbb{P}()$. In this case, and are negatively correlated.
  3. $\mathbb{P}(∣) = \mathbb{P}()$ if and only if $\mathbb{P}(∣) = \mathbb{P}()$ if and only if $\mathbb{P}(∩) = \mathbb{P}()\mathbb{P}()$. In this case, and are uncorrelated or independent.

However, there is still no numerical definition of correlation between events.

What is the numeric formula definition of correlation between events? Is it a number between -1 and 1?

iluvmath
  • 205
  • There are many quantitative ways to measure the sense of "correlation" generally. The most obvious in this case is to use your favorite measure of the correlation of the indicator functions for the events. This goes under various names and has several equivalent numerical expressions. See https://stats.stackexchange.com/questions/103801, which I view as being the same question asked in a different way (because events and their indicators are equivalent things). – whuber Aug 29 '22 at 16:36

0 Answers0