Resolved: What is the average in expected values?
since we are multiplying with the probabilities of each event, where does average accounts for in this definition?
Thank you for your question!
If I understand correctly, you are confused about the definition given at the beginning of the lecture, namely, 'the average outcome we expect if we run an experiment many times'. If that is the case, then it would be easiest to explain this through the darts example given at the end of the video. Imagine that you perform 10 throws and these are your results:
5 times you got 10 points;
4 times you got 20 points;
1 time you got 100 points.
Taking the average of this results (summing all the points and dividing by the total number of throws) gives you:
(5 * 10 + 4 * 20 + 1 * 100) / 10 = 230 / 10 = 23.
Therefore, even though you can't score 23 point, your average result is 23.
Hope that answers your question!