Activity for thelast19digitsofpi
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #282038 |
(2) We don't know the number of people, but for most of the calculations it doesn't matter. Let's say there are 1000. 50% are married, so 500 are married and 500 are not. Out of the 500 married people, 10% **of 500 married** people smoke, which is 50. 30% **of non-married people** (of which there are... (more) |
— | almost 3 years ago |
| Comment | Post #282038 |
(1) Ah, I see. The words "to smoke" apply to both "married" and "average person". In probability notation it's Pr(smokes | married) < Pr(smokes), where Pr(X | Y) means "probability of X given Y is true". (Some sources just use "P" instead of "Pr".) (more) |
— | almost 3 years ago |
| Edit | Post #282049 |
Post edited: Fixed formatting of dollar signs |
— | almost 3 years ago |
| Suggested Edit | Post #282049 |
Suggested edit: Fixed formatting of dollar signs (more) |
helpful | almost 3 years ago |
| Edit | Post #282043 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: De-mystifying tricks – If $\{x_n\}$ converges, then Cesaro Mean converges. There's a lot going on here, so I'll start with some overview. It looks like the idea of the proof is to split $1,...,n$ into two pieces, where the first piece is of fixed size $C$, and the second piece has average close enough to $L$. The first piece has fixed size but the second piece can be made s... (more) |
— | almost 3 years ago |
| Edit | Post #282041 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How can I visualize $\lim\limits_{x \rightarrow \pm \infty} f(x) = \lim\limits_{t \rightarrow 0^{\pm}} f(1/t)$? I'm not sure if it's really possible to visualize it without creating another graph, but what you could do is take a function, like f(x) = sin(2x²)/2x², and graph f(x) and f(1/x) on the same graph. Notice how the peaks and valleys of the red function, f(x), and the blue function, f(1/x), correspond t... (more) |
— | almost 3 years ago |
| Edit | Post #282038 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How to quantify "married people are less likely than the average person to smoke", "smokers are less likely than the average person to be married"? Let's consider 2.1 first. You said that married smokers smokers, but now married smokers / married people is 10%, and all smokers / all people is 20% (check this yourself). I wonder if you meant to write married smokers < all smokers, which is the same kind of error as for equation 2.1 if you swi... (more) |
— | almost 3 years ago |