3 ms·

Have you actually studied calculus based probability/stayistics though? Your comment seems characteristic of my own former thinking from when I had only taken a

Have you actually studied calculus based probability/stayistics though? Your comment seems characteristic of my own former thinking from when I had only taken an algebra based intro stats course (AP statistics) and hadn't yet learn it the calculus based way a few years later. There is a lot of cool stuff you miss out on in the basic stats course because of having to dumb it down to avoid the calculus. Some I remember off hand: - proof of the central limit theorem, which gives the shocking result that if you sum several uniform distributions you get rapidly more precise approximations of the normal distribution, which looks similar to exp(-x^2) if I recall. This central result is the foundation of all statistical sampling. This is why in real life if you see something follow a normal distribution you can guess it is probably caused by a moderate to large number of somewhat independent factors, and vice versa. This is genuinely useful, but if you don't know it you won't miss it - poisson distribution which relates the mean time between events to the probability of failures. Obviously very applicable to a lot of real life tbings

galdosdi 4y ago
Also, pretty much every fancy formula you learn in Stats 100/ AP stats that looks weird but is very useful, can be derived and proved using calculus. Without calculus you just have to take it on faith, and may not have as intuitive an understanding of why it's true and what the significance of the terms is. The same is the case in basic physics. No, V does not = IR, nor does F = ma. That's the simplification they tell us so they can explain a simplified version to us. In fact, the correct equations have derivatives in them and thus are differential equations. Look, nobody needs calculus but nobody needs to read either. After all you could hire someone to read everything out loud to you. All knowledge is like this.

galdosdi 4y ago

Also, pretty much every fancy formula you learn in Stats 100/ AP stats that looks weird but is very useful, can be derived and proved using calculus. Without calculus you just have to take it on faith, and may not have as intuitive an understanding of why it's true and what the significance of the terms is. The same is the case in basic physics. No, V does not = IR, nor does F = ma. That's the simplification they tell us so they can explain a simplified version to us. In fact, the correct equations have derivatives in them and thus are differential equations. Look, nobody needs calculus but nobody needs to read either. After all you could hire someone to read everything out loud to you. All knowledge is like this.