Metro mean and variance

At the metro every few weeks I run into a nice example of the relationship between mean and variance. My card is running out of credit, so I figure I should recharge it. Now, should I do that before the train ride, or after?

If I recharge the card after the ride, it will take one minute, and that’s that. The mean time spent is one minute and the variance is zero.

If I recharge it before, it’s a lottery. Nine times out of ten, I’ll catch the same train, so I’ll lose zero minutes. The tenth time, I’ll miss the train and spend ten minutes waiting for the next one. The mean is exactly the same, one minute! — but the variance is far from zero.

So which is the right choice? Ah, that depends on my day’s schedule and my mood and my personality. There’s nonlinearity for you.

[24 March 2018]

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