As for why I was confident, well, this was a clear (in my eye at least) example of Jensen’s inequality: we are comparing the mean of the log to the log of the mean. And, if you see this inequality come up often, you know that the inequality is always strict, except for a constant distribution. That’s how I knew.
As a last note, I must praise the fact that you left your original comments (while editing them of course) instead of removing them. I respect you a lot for that.
I apologize, my wording was indeed rude.
As for why I was confident, well, this was a clear (in my eye at least) example of Jensen’s inequality: we are comparing the mean of the log to the log of the mean. And, if you see this inequality come up often, you know that the inequality is always strict, except for a constant distribution. That’s how I knew.
As a last note, I must praise the fact that you left your original comments (while editing them of course) instead of removing them. I respect you a lot for that.