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One of the biggest challenges in learning, especially in learning something new, is that it’s a chain. If you don’t have something’s prerequisite knowledge, you
by travisjungroth 3y ago
One of the biggest challenges in learning, especially in learning something new, is that it’s a chain. If you don’t have something’s prerequisite knowledge, you can’t understand it (by definition). This means that only one insufficient explanation by the author blows it. As a general rule, it’s really hard to not mess up once!
You make a good distinction between someone being paid to respond and not. A feedback loop helps out a lot here.
Failing that, you need to take this into your own hands. Honestly, you’re probably going to have to tell yourself a new story to get there. Maybe having empathy for the difficulty of teaching. Maybe it’s finding some inner drive. I don’t know. But you need to look at that paragraph, accept it’s insufficiently explained, and take responsibility for understanding it.
I’m not saying to read it over and over until you “get it”. (I don’t know why people try that, it’s kinda foolish). A simple strategy works most of the time. Read it until you find a word or phrase you don’t sufficiently understand. Maybe that’s “random variable”. Maybe it’s “probability density function”. Find an explanation for that (Wikipedia, ChatGPT, textbooks, videos). The fun thing is this algorithm is recursive. So you’ll likely run into something you don’t know again. That’s okay, just keep going. If it’s really tough, a lot of the value of a tutor is steering this depth first search.
Get each concept to the point you understand it very well for the problem at hand. You don’t have to know everything about PDFs, but don’t hand wave it either. After this process, you’ll be able understand this paragraph and continue.
This may take a while! If something is in a new domain, it’s usual for you to actually spend more time backfilling knowledge than on the main content itself. That may make it not worth it for you, but it’s not inherently bad. And the next time for something similar should be faster.
- syntaxfree 3y agoThe pdf is just the pullback measure. A random variable is a function X(w) taking (eg) real values. In your probability space you already have an ambient measure space and an ambient probability measure P which takes sets in the measure space to [0,1]. The pdf is then the function defined on sets P(invX(q)). invX is a set valued inverse. Ok, consider coin flips. Then X takes each element of sample space either to 1 or -1. Set values inverse of 1 is the sets that map to 1. Then we get the ambient probability measure of them. You don’t really have to cope with measure theory in full to take this tiny step.
- travisjungroth 3y agoI don’t think the set of people who couldn’t understand the quoted paragraph but could understand your comment is very large.
- patrick451 3y agoI'd be shocked if somebody knows what an ambient measure space is but doesn't understand the nth moment of a random variable.
- rhymer 3y ago1/ I think you are referring to pushforward measure (https://en.wikipedia.org/wiki/Pushforward_measure https://en.wikipedia.org/wiki/Pushforward_measure): the random variable "pushes" the probability measure to its codomain. 2/ pdf requires a stronger condition: the pushforward measure needs to be absolutely continuous with respect to the sigma-finite measure (usually the Lebegue measure) on the codomain.