I’ll start you off with two puzzles. Their relevance should become clear by the end of this post:
• Puzzle 1. Suppose I have a box of jewels. The average value of a jewel in the box is $10. I randomly pull one out of the box. What’s the probability that its value is at least $100?
• Puzzle 2. Suppose I have a box full of numbers—they can be arbitrary real numbers. Their average is zero, and their standard deviation is 10. I randomly pull one out. What’s the probability that it’s at least 100?
Before you complain, I’ll admit: in both cases, you can’t actually tell me the probability. But you can say something about the probability! What’s the most you can say?
Some good news: Brendan Fong, who worked here with me, has now gotten a scholarship to do his PhD at the University…
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