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Yep, except to avoid ambiguity: p_m is the probability of it taking exactly m throws to obtain the first string of n consecutive heads.

As with most of the things that I post here, this is a little tricky. (But it is in the easier 50% I reckon.) I think a past HSC or well known trial question 8 has asked something like this with n=2? It seems vaguely familiar.

Not quite, the answer isn't that simple. (Also if you think about what the question is asking, it cannot be < 1).

A man tosses a fair coin repeatedly until he throw n heads in a row. (n a positive integer). What is the average number of tosses required? If you cannot solve the general problem, feel free to post solutions for small values of n.

He is multiplying both numerator and denominator by a product of even numbers which "fills in the gaps" in the factorial in the denominator. 2.4.6....(2n+2)

Re: HSC 2014 4U Marathon Well, they only aren't in the syllabus in the sense that some of them are harder than any question the bos would set in an actual HSC paper. They don't need any theory from outside the mx2 course to do.

I didn't think that students were allowed to state/use AM-GM without proof?

A lot of friends have asked me why the standard of rigour in mathematical proof is so high. Why it is necessary to fiddle with things like epsilons and deltas? Why do people waste their time looking for proofs of theorems that we have verified up until massive numbers using computers? Eg...

Re: yasminee96's raw marks Adv English and Biology Weird that "raw" is actually scaled in some way.

Re: yasminee96's raw marks Adv English and Biology How do those marks in individual english sections give you a raw mark of 89/100? Is it calculated in some weird way other than just looking at (total)/105?

Voted no, but its entirely individual. If you don't back yourself to perform well in your 10 best units then you haven't done enough preparation.

1. We say that our cell-phones are designed because WE designed them, not because they are complex. We have a precise history of the invention of the cell-phone. Observing an object with properties A and B is not a shred of evidence for the assertion A=>B. Could you please elaborate on "general...

Why should complexity imply design? I don't see how this follows at all. I also really don't find arguments based on improbability convincing mostly because http://rationalwiki.org/wiki/Improbable_things_happen. Sure it is improbable that the sequence of scientific accidents required for us...

page 666, yay satan.

Re: HSC 2014 4U Marathon Let f be a real-valued function defined on R. For which values of the real constant p does the inequality below imply that f is twice differentiable? |f(x)-f(y)| =< C|x-y|^p for all x,y. C a constant. Justify your answer with proof.

Okay sure, I agree with you there. It's just not that common in that extreme I feel. Care to elaborate? Well if that "normal" is more alert than their previous "normal" I see nothing wrong with it. Perhaps I am slightly biased here because I like many people in academia run off coffee and tea...

Who are you quoting here, I have met a lot of people who smoke in my life, some really regularly, but can't recall even one person suggesting that everyone needs to do it. As a matter of fact they tend to be more open-minded and less judgemental about other people's lifestyle choices than the...

You can't put things like that down to weed because there are so many other factors, chiefly how driven the person is. If he is smart but really doesn't give a fuck then of course he won't do as well as he "should." I smoked quite a bit back in yr12 and early uni and did just fine.

Weed is pretty harmless and fun. I have actually had some pretty cool creative mathematical ideas under the influence, though I get a little slower at the nitty-gritty. Certainly less bad for you than alcohol. I also think that everyone owes it to themselves to experiment with some kind of...

Re: HSC 2014 4U Marathon Imagine a rectangular grid with n! rows (one for each permutation of the students), and n columns (one for each student.) Put a counter on each square in the grid such that the corresponding student is fixed by the corresponding permutation. Then the LHS is clearly...