Tropers that do NOT hate math

[1] Shame the last message in this thread is almost a year old, because I would‘ve been in support of LaTeX integration.

I‘m currently preparing for a retake of a statistics exam, and the amount of stuff we need to memorize is giving me trouble, especially because I never had to memorize anything in high school maths classes. As an example, here‘s an exercise I‘m currently working through:

A broken machine fabricates cubes with a uniformly(1, 2) distributed edge length. Let X _i, i ∈ N be the edge length of the i‘th cube, and all cube sizes are independent. Find the almost certain limit:

$\lim_{n -> \infty} \frac{1}{n} \sum_{i=1}^n X_i^3$

My intuition says that‘s the average size of a cube, which would evaluate to (3/2)^3, and I have some broad ideas of how to formalize this - something with the law of large numbers and the average of the uniform distribution of (1,2) is 1.5, but then when I check the solution it mentions some cursive L^4, and I‘m scared.

OMG, a new post in this thread!

Sadly, I don't understand enough about the concept you mentioned to offer any input of my own. XP

Late to the party, but here's a link that might help. The point is, the average of the multiple of two random variables is not the multiple of the average of the random variables. I.e., mean(x)^3 is not mean(x^3).

What you have to do, then is to use the formula for the expected value of a continuous random variable.

So here's an interesting homework exercise - I'm not gonna spoil what it is just yet, but it does end up being fun and fascinating:

Let f: R->R be a differentiable function with f'(x) = f(x). Find a Taylor series for f at the point 0. For which x does this series converge?

And once you‘re done with that, plug 1 into the Taylor series, calculate a handful of the summands, then look up the number you get as a result in Google.

Shh, spoilers! I know f‘=f is a dead giveaway for those who know, but still.

Edited by StepexNo2 on Mar 27th 2024 at 7:27:02 PM

It's e^x

I know that f'=f is a dead giveaway, but still. It's the process that matters, right?

Oh by the way, how did your statistics exam go?

Poorly. I did not learn my probability distributions on time, so I figured I didn‘t have a chance anyways

...Ah, man.

While I STILL can't answer this level of question, now I at least know what the terminologies in the question actually mean,

A progress is a progress, I guess.