eli5: Do expected values of various kinds of discrete probability distribution always have the highest probability?
In: 3
No.
We have a random variable that can take on three values 1,2, and 3.
1 and 3 have a 40% probability and 2 has a 10% probability.
The expected value is 1×0.4 + 2×0.1 + 3×0.4=1.8.
Not only is the EV closest to the least probable value, it’s not even a value the distribution can take on at all.
Hell, consider even a uniform distribution. The EV of a standard die roll is 3.5.
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