Calculus might not be the best example of a skill with relatively low payoff, because you need some calculus to understand what a continuous probability distribution is.
I do? I thought I understood both calculus and continuous probability but I didn’t know one relied on the other. You are probably right, sometimes things that are ‘obvious’ just don’t get remembered.
For example, suppose you have a biased coin which lands heads up with probability p. A probability distribution that represents your belief about p is usually a non-negative real function f on the unit interval whose integral is 1. Your credence in the proposition that p lies between 1⁄3 and 1⁄2 is the integral of f from 1⁄3 to 1⁄2.
Calculus might not be the best example of a skill with relatively low payoff, because you need some calculus to understand what a continuous probability distribution is.
I do? I thought I understood both calculus and continuous probability but I didn’t know one relied on the other. You are probably right, sometimes things that are ‘obvious’ just don’t get remembered.
For example, suppose you have a biased coin which lands heads up with probability p. A probability distribution that represents your belief about p is usually a non-negative real function f on the unit interval whose integral is 1. Your credence in the proposition that p lies between 1⁄3 and 1⁄2 is the integral of f from 1⁄3 to 1⁄2.
Yes, extremely obvious now that you mention it. :)