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One benefit to defining the codomain of a random variable as a (real) number because it makes defining the expectation of a random variable easier to understand
by tylerhou 2y ago
One benefit to defining the codomain of a random variable as a (real) number because it makes defining the expectation of a random variable easier to understand. (Of course, it is possible to define the expectation more abstractly, but people who study probability often have not taken an abstract/linear algebra course.)
- eru 2y agoYes, I agree about the pedagogic benefits. Though as kazinator demonstrates in this thread, it looks like this approach can lead to some confusion between random variables and expected values.