I'm trying to replicate some math a professor did related to Twitter sentiment analysis. Basically, there is a sentiment dictionary, called ANEW, that contains a mean and standard deviation for 3 different types of scores: valence, arousal, and dominance. The link above is to the page with a full description (with the germane math being 3/4 of the way down). The pertinent section is also available here, in this image:
I understand what he did with calculating the overall standard deviation. However, I do not understand what he did with calculating p(sub-i) in the second set of equations. It looks like he's taking the product of a series, but what series? If I plug in a value for i, then am I not just getting p for the standard deviation of the valence value at position i?
I have tried to reproduce his example in the final paragraph at least 4 or 5 different ways, but I never end up with the same values. Given the values presented in the final paragraph of the image, can somebody walk me through how to calculate the overall weighted average of the valence for the tweet presented?