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Energy trading quant here. If anyone interviewed me with this crap I'd walk out immediately.
Care to elaborate? I guess those Ramanujan-like infinite series are a bit like trivia questions, right? Does anyone really have an intuition to solve something like that?
Here's my favorite interview question (spent 10 years as a quant, interviewed a bunch of people, most do not do well on this) We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result. I do the same. You do not know whether I've re-drawn and I do not know whether you've…
This seems so simple. Decisions and draws are independent - we can ignore the other guy and just go for the highest value. Draw the first number. If it's below 0.5, draw again, since the odds then are that the next draw will be higher. Is there more?
Now, you get. 0.500001 on your first turn. There is a 25% chance they got less than 0.5 so you win 25% of the time. Well, if they are randomly under 50% then you have a better than 75% shot of beating them with a reroll. (50% your over 0.5 and thus win and 25% you are under 0.5 and still win.)
But, they are above 0.50 then you gain a 25% chance of beating them (coin flip for over 50% and 50/50 odd or 50% of a loss) your under 50% and have even odds. Thus, you go from 25% win chance to .25 * .75 + 0.75 * 0.25 or 0.375% which is better odds for re rolling.
Earlier quoted context omitted.
No, I did mean everyone. Or everyone who cares about understanding the world. Or rather, everyone who cares about understanding the world they themselves should be wanting to learn more maths than just sums and multiplications. Anyway, thanks for the feedback.
| everyone who cares about understanding the world. Those fluent in math really need to drop this egocentric view. If you can't do matrix manipulations you aren't curious about the world? Give me a break. The breadth of topics that yield understanding of various parts of our world is vast. Do you have an early university understanding of history, politics, math, sociology, psychology, economics, law, capitalism, etc.…
Earlier quoted context omitted.
This seems so simple. Decisions and draws are independent - we can ignore the other guy and just go for the highest value. Draw the first number. If it's below 0.5, draw again, since the odds then are that the next draw will be higher. Is there more?
That was my analysis as well. What the other guy does is unknown and therefore irrelevant. If you can improve your current expectation, you do. You can trivially search over that strategy space and see that, yep, 0.5 is the maximum. #include #include int main(int argc, char *argv[]) { for (double d = 0.25; d
[1] probably has to do with the probability distribution having a shape more interesting than a Gaussian bell
Earlier quoted context omitted.
It isn't. There's a clear, well defined answer.
I'm just a programmer, but this seems really easy to me. What am I missing?
Here's my favorite interview question (spent 10 years as a quant, interviewed a bunch of people, most do not do well on this) We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result. I do the same. You do not know whether I've re-drawn and I do not know whether you've…
Alternative option: spend time on other things because quants are about the big bucks
Here's my favorite interview question (spent 10 years as a quant, interviewed a bunch of people, most do not do well on this) We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result. I do the same. You do not know whether I've re-drawn and I do not know whether you've…
Here's my favorite interview question (spent 10 years as a quant, interviewed a bunch of people, most do not do well on this) We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result. I do the same. You do not know whether I've re-drawn and I do not know whether you've…
Oh my god it's the golden ratio! That's so cool! EDIT: I'll show my work, rot13'd... Jr pna cnenzrgrevmr n fgengrtl ol n guerfubyq g: gur inyhr gung gur svefg qenj arrqf gb or yrff guna va beqre gb pubbfr gb qenj ntnva. Hfvat guerfubyq g, gur cebonovyvgl bs trggvat yrff guna g vf g^2 orpnhfr lbh unir gb qenj orybj gur guerfubyq gjvpr va n ebj. Gung chgf gur cebonovyvgl bs raqvat hc nobir gur guerfubyq ng 1-g^2. Gur c…
Edit: thanks. This is convincing, but... given that we're looking for a fixed point of a process like... [bah, I lack words to describe a vague, non-rigorous intuition]... I expect that there is a convincing one-sentence explanation that also shows it to be the golden ratio. Am I wrong? Can anyone give a simpler explanation?
Here's my favorite interview question (spent 10 years as a quant, interviewed a bunch of people, most do not do well on this) We're going to play a game. You draw a random number uniformly between 0 and 1. If you like it, you can keep it. If you don't, you can have a do-over and re-draw, but then you have to keep that final result. I do the same. You do not know whether I've re-drawn and I do not know whether you've…
This seems so simple. Decisions and draws are independent - we can ignore the other guy and just go for the highest value. Draw the first number. If it's below 0.5, draw again, since the odds then are that the next draw will be higher. Is there more?
For example, consider a similar game where you draw and then optionally re-draw (like in the original game) but the amount of money you win if you end up with a number p is p if p 0.8, where b is some constant. Then you're also trying to "go for the highest value". However it is clear that in the limit of large b, your best strategy is to redraw if p < 0.8.