Dear CraigMichael,
I am by no means a guru. It seems like you prefer Apollo Creed problems to Clubber Lang problems because you’re more able to motivate yourself to do Apollo Creed problems. I feel the same way. I find it exciting to start new projects, and grueling to continue my existing projects. My advice:
If you need to solve a Clubber Lang problem, then in moments of clarity, you should establish habits/systems to solve the Clubber Lang problem that don’t require you to be motivated on any given day.
E.g. go for a jog even when you’re not feeling motivated to go for a jog, because you set out your jogging clothes and shoes the night before, & you made a program to pay your rival $5 on venmo if you don’t log your jog on MapMyRun.com
Wishing you the best,
CTVKenney
The VARIANCE of a random variable seems like one of those ad hoc metrics. I would be very happy for someone to come along and explain why I’m wrong on this. If you want to measure, as Wikipedia says, “how far a set of numbers is spread out from their average value,” why use E[ (X—mean)^2 ] instead of E[ |X—mean| ], or more generally E[ |X—mean|^p ]? The best answer I know of is that E[ (X—mean)^2 ] is easier to calculate than those other ones.