Ask HN: What's your speciality, and what's your "FizzBuzz" equivalent?

  A-->   +--[1 Ω]--+--[1 Ω]--+
         |         |         |
       [1 Ω]     [1 Ω]     [1 Ω]
         |         |         |
         +--[1 Ω]--+--[1 Ω]--+
         |         |         |
       [1 Ω]     [1 Ω]     [1 Ω]
         |         |         |
         +--[1 Ω]--+--[1 Ω]--+    <-- B

You pass.

Q: "Something you have no experience with has broken and won't do a basic function, how will you go about fixing it?" A: Research, ask someone else etc.

Q: "X is missing their password for a system we have no admin rights on. How are you going to fix this?" A: Recovery Tools. Format device and set it up again. Use JS/Developer tools to get it in plain text from the browser.

    find /path/to/wherever -name "*.mp3" -delete

    cd /path/to/wherever
    rm -rf *.mp3

?

  find path -iname "*.mp3" -print0 | xargs -0 rm -fv

    find /path/to/wherever -name "*.mp3" -delete

These two functions are not separate.

In my own experience the marketer's primary job is to identify how and why your end-users might use your product, i.e. understand who these qualified leads are to begin with.

    var foo = function (n) { return foo(n); }; foo(1);

    var factorial1 = function(n) { return n < 1 ? 1 : n * factorial1(n-1) }
    
    function factorial2(n) { return n < 1 ? 1 : n * factorial2(n-1) }

That is to say, this question has worked for us as a dev house, maybe not so much if you're hiring contractors, I can't say for sure.

    var func = function(){};
    function func(){};

However they're probably wondering if the user knows about scope and other such things. Inside the brackets we have a new scope but it has access to top level scope as well. They want to know that you know that stuff.

Try any of the two lines above in a js console (in browser) then type:

    window.func
    this.func
    func

  var func = function func() { /* blah */ };

  function func() { /* blah */ };

I feel like the mechanics of test selection biases against people who've specialized in Bayesian stuff—which might be very interesting! It's definitely a make-or-break kind of thing as to whether you can correctly formulate all the various moving parts and relate them correctly.

That said, I also wouldn't expect someone to write out implementations on a whiteboard under pressure (I'm not a Google recruiter). I'd be more interested in prodding their brain to gauge their general level of understanding, which is (I'm pretty sure) how hiring committees for mathematicians in academia operate. If they have a good foundation, I think it's less important that they've rote memorized implementation details.

Honestly, after a certain amount of time, I'd expect a new hire would be able to teach me what is state-of-the-art in the field based on new literature.

But the questions I'd have in mind would be couched like this:

Linear system:

    - Is it small, square, and numerically well-conditioned? Use LU - it's pretty fast to write and pretty fast to use in practice.

    - Is it small, but rectangular (ie. overdetermined), or not as well conditioned? QR is a good choice.

    - Is it small, but terribly conditioned, or do you want to do rank revealing, or low-rank approximation while you're at it? Will you be using this matrix to solve many problems (multiple right-hand sides)? SVD would fit the bill

   - Is it large, or sparse, or implicitly-defined (ie. you don't actually have access to the elements of the matrix defining the system - you just have a surrogate function that gives you vectors in its range, or something)? Use an iterative algorithm. Krylov subspace methods (MINRES, GMRES, conjugate gradient, etc) are your friends here.

    - If you wanted to determine the "strength" of a waveform (in a finite uniform sampling of data) that is re-occurring in a fairly regular way (like arterial pulse in an array of data taken from an oximeter), what type of transformation would you use, and how would you use the resulting information given in transform domain?

   - What if you wanted to determine the strength of a waveform that is short lived/impulse in nature, but re-occurs without any known periodicities (eg. eye blinks artifacts in a sample of EEG data)

   - How would your answers to the above questions change if there are n separate channels of data collected simultaneously (ie. sampled in different locations), which may be analyzed together?

    - What does statistical significance mean, in the context of decision making? Is it a property of the test you perform, or is it a property of your data? (sort of a trick question, this basically rehashes the Fisher vs. Neyman & Pearson debates of the 20th century stats community)

   - Some cod problems of when to use z, t, f tests. Basically, you use them when your situation matches the appropriate inference models (two normally-distributed sample comparison of means with identical variances? t test.)

   - How do you construct an optimal test from scratch, if one doesn't already exist for your particular situation? (basically, if minimize type II error with fixed type I makes you comfortable for your problem, can you do use the Neyman-Pearson lemma to do likelihood ratio construction correctly)

   - What does a p-value actually mean? What if you instead wanted to have actual probabilities for your hypotheses, or you had apriori information that you wanted to use? (Bayesian inference is the winner here)

   - Probably something from point estimation: least squares, minimax criterion, Bayesian MAP estimates, general model fitting, those sort of thing. Brings it all back around to numerical (where I'm most comfortable). Like how applying statistical ridge regression is just knowing how to code up Tikhonov regularization, when you get down to implementation.

Classical Arabic and other semitic languages are VSO, but spoken Arabic is mostly SVO.

Edit

You're right that it would be (somewhat) impressive if they knew there was a transition.

The short answer is "pretty well." Usually I ask specifically for major comma rules, which I'd tend to define as:

* Connecting independent clauses with a conjunction * As part of a list * To offset a word or phase at the start of a sentence. * Like parentheses (or, in the lingo, an appositive phrase).

If they say, "I have no idea," that's a very bad sign; if they ask questions like yours, that's a good sign.

A fun, short book called Write Right! by Jan Venolia is worth reading if you're interested.

I like this question because the base query, however you interpret the unclear parts, is easy, but it still allows candidates to impress me by asking about the "edge" cases. And even if they just makes assumptions, I can still ask them to do the other versions to see if they really know what they're talking about. I'm always amazed at how many people can't convert an inner join to a left join, or can't change a sum() to a count().

Something like this could work (without going for an alternate approach such as Unions or sub-selects):

    SELECT a.name, ISNULL(SUM(s.price), 0.0) FROM authors a
    INNER JOIN books b ON (a.id=b.author_id)
    LEFT OUTER JOIN sales s ON (b.id = s.book_id)
    GROUP BY a.name, s.date
    HAVING (ISNULL(s.date, '20131101') >= '20131101' AND ISNULL(s.date, '20131101') <= '20131130')

The chance of picking the biased coin is 1/1000. The chance of seeing 10 heads from a fair coin is (1/2)^10 = 1/1024. These are nearly equal, so given that you've seen 10 heads, there is a 50/50 chance of having a biased coin. So the probability the next flip shows a head is

  P(H) = P(biased) * P(H|biased) + P(fair) * P(H|fair)
       = 0.75

Yo want to figure out P(biased | 10H). Using Bayes rule this is

  P(biased | 10H) = P(10H | biased) * P(biased) / P(10H)
                  = P(10H | biased) * P(biased) / (P(10H|biased) * P(biased) + P(10H|fair) * P(fair))
                  = 1 * (1/1000) / (1 * 1/1000 + 1/1024 * 999/1000)
                  ~ 0.5

When we have the double heads coin, the probability of getting 10 heads is 1: P(10 heads|fake) = 1. When we have a normal coin, the probability of getting 10 heads is P(10 heads|fair) = 0.5^10.

The quantity we want to compute is

    P(heads|10 heads) = P(fair|10 heads)*0.5 + P(fake|10 heads)*1 
                      = P(fair|10 heads)*0.5 + (1-P(fair|10 heads)) 
                      = 1 - P(fair|10 heads)*0.5.

    P(fair|10 heads) = P(10 heads|fair) * P(fair)/P(10 heads)

    P(10 heads) = P(10 heads|fake)*P(fake) + P(10 heads|fair)*P(fair) 
                = 1*0.001 + 0.5^10*0.999.

    P(fair|10 heads) = 0.5^10 * 0.999 / (1*0.001 + 0.5^10*0.999)

    P(heads|10 heads) = 1 - 0.5^10 * 0.999 / (1*0.001 + 0.5^10*0.999) * 0.5 
                      = 0.75308947108

http://yudkowsky.net/rational/bayes

Useful if you want to know (or need a good way to explain) what a posterior probability is and how it's different from a prior probability

I like a "factor label" style approach where you can see the prior probability (Fair: Biased), the information about the flips, and the posterior probability (the revised chances after the new information is taken into account):

Prior * Information = Posterior

so

(Fair : Biased) * (10 Fair heads : Fair ) : (10 Biased heads : Biased) = 10 Fair Heads : 10 Biased Heads

Plugging in, we'd have:

(999 / 1) * (1 / 1024 ) / (1 / 1) = 999 / 1024

The odds are ever-slightly in favor of a biased coin. So we can mentally guess ever-slightly above 3/4 for the chance of another heads. We could write (999/2 + 1024) / (999 + 1024) on the whiteboard to be exact.

You'd be surprised at how many people can't answer instantly. Or how many people can't give a convincing description of what a share is, and what rights it gives you.

These are all easy questions, which to my mind is the point. The fact that someone can answer them doesn't tell you much, but if someone can't answer them then you need to think very hard about whether to hire them.

* The person suggesting the question says that this is trivial for people suited to the job in mind;

* You say you couldn't do this question;

* You also say that you would be suitable to do the job.

Given that the proposer of the question is the one that understands the job, I'm having a hard time understanding why you claim you would be suitable for it, given that you couldn't do the question. Please understand that I'm not attacking you specifically, I'm just having a hard time understanding your reasoning.

The negative sign is your stubborn conviction about the lack of value of rote memorization.

The stereotypical "rote learner" you describe in your before-last paragraph is just as one-sided as the opposite.

Of course neither extremes really exist and you probably have rote-memorized more things than you realize. You don't work out everything from scratch every time you encounter a medium hard problem.

Unless you actually do, in which case someone reasonably clever who does not stubbornly refuse to learn a few formulas will beat you by speed. Which is a reason to hire them over you.

That's the the point. You may be very smart and capable doing it this way, but learning a few basics (such as Bayes, in the context of statistics) doesn't really cost you anything. Memorizing a few things isn't hard. You won't actually run into problems like "erroneous thinking" because you're smart enough and knowing the conditions under which something holds is easy enough when you understand the thing. Additionally you get the knowledge when a particular important theorem does not hold, which is higher level knowledge that you just can't get when you reason from scratch every time (positive vs negative knowledge).

Memorizing a few of the basic important theorems and formulas in your field is such low-hanging fruit to improve yourself that a potential employer might ask why you're not doing it, even if you're so very capable without doing it.

Finally, there's communication with your peers. Maybe you can figure that stuff out by yourself easily, but when your colleagues say "ah, so we just use Bayes and poof", you'll be lagging behind figuring that out, and in reverse when you do these things from scratch, I'm assuming you'll be doing them much quicker, speeding through your ad hoc methods, leaving your team mates confused and wondering "why don't he just use Bayes?" (which may or may not be what you are in fact doing, but you lack the knowledge to tell them as much).

I'm sure you do a very good job at what you're doing now, the way you're doing it. I'm just pointing out that there are various well-justified reasons why employers can be wary of your refusal to memorize some basic field-knowledge, even when you're perfectly capable figuring out that stuff when you need it.

You're assuming an underlying model for the data. You have a test statistic( that estimates a model parameter) and you have a hypothesis regarding a parameter. The p-value is the probability that you get a test statistic more extreme than the one observed assuming that your hypothesis is true.

Ex. You have a sample of 1000 men's heights. You compute the sample average height as 5'9 and a sample standard deviation of 3 inches.

(Unlikely) hypothesis: the average height is 4 feet. Your p-value is the probability of getting an sample average more extreme than 5'9 given that your 4 ft height hypothesis is true. Given that the sample standard deviation is 3 inches and 5'9 is 7 standard deviations from 4ft... the p-value is going to be small, so you'll reject that.

Note: I'm leaving out details and assumptions

But the product is also a^(p-1).(p-1)! by commutativity. So a^(p-1)=1 (mod p).

There's a clever idea in there, to consider prod(ka) for fixed a and k=1..(p-1). Not finding the clever idea means you won't prove it. Finding the clever idea is tricky. Once you know the clever idea the proof is trivial.

The DOM API isn't very large/complicated, and it shouldn't be hard to MOSTLY memorize it. It isn't a "gotcha" question though, a good interviewer is not gonna ding the heck out of you if your forget bits of it (most web devs do spend most of their time with jQuery, YUI, etc after all) - it's about whether you understand what's going on behind the scenes.

After all, I often have to look up a rarely used method. Seems unfair to judge harshly if they do so.

I suppose there are people out there that are working as front-end developers for websites that only work in HTML and CSS, but I would think that's getting more rare as time goes on. Of course, that could just be bias based on my own career.

But, going with your suggestion as a thought exercise, I would go in a different direction. To make a pattern like fizzbuzz I suppose I would do something more like: build a page with a series of paragraphs so that these CSS properties apply to every third paragraph, these CSS properties apply to every fifth paragraph, and so on. Something possible with CSS but requires the ability to think things through.

Luckily he didn't specify the dimensional requirements, so we can get away with f^[0] = f[0].