mb12777

Haha, well thanks for a reply. It does get pretty confusing at times, and plain boring at other times.

Bump it up... I'm still clueless on this, I've tried googling it as well. Can anyone help at all?

So I've recently come across a statistics problem that interested me, and it's not covered at the level I'm currently being taught at (my teacher still wants me to have a go at it). I'm guessing it'll be easiest if I just post the question and where I'm up to. Q: X and Y are independent random variables with variances 4 and 12 respectively. Find the correlation coefficient between 2X+Y and 5X-Y. Where I'm up to so far X~N(x, 4) and Y~N(y, 12) (I'll use x and y as the means, I don't know how to get the actual symbols) So call 2X+Y A, and 5X-Y B, then A~N(2x+y, 28) and B~N(5x-y, 112) I'll just say that there were n numbers taken from each distribution Then I got Saa=28n, and Sbb=112n, so the denominator for the correlation coefficient should be the square root of 28n*112n, which comes out as 56n. So I already know the denominator is 56n (I'll also use {Sum} in place of a summation sign, again I don't know how to get those on here) Where I'm stuck is at finding the numerator. I expanded out Sab={Sum}(ai-a)(bi- to get this... Sab= {Sum}aibi - b{Sum}ai - a{Sum}bi +ab But {Sum}ai = a*n, and similar for {Sum}bi So then Sab = ab - 2abn + {Sum}aibi => Sab = ab(1-2n) + {Sum}aibi Now, at this point I'm thinking I could just find the mean of A*B, and multiply this by n to get {Sum}aibi. But I have no idea how I could find a distribution for A*B, all I know is I can't simply multiply the means of each distribution. I hope this made sense, and any help would really be appreciated.

So the title is fairly self-explanatory. If the critical value is exactly the same as the test statistic in a hypothesis test, should the null hypothesis be accepted or rejected?

Sorry to keep bothering you, one last question! So I've got 5/4 [0.5sinh(2u) + u], that's with a lower limit of 0 and an upper limit of sinh-1(2/√5). I get that sinh(sinh-1(2/√5)) would be 2/√5, but it's sinh(2u) instead of sinh(u). Now, when I put this all into my calculator for 2u, I got an answer of exactly 2.4.... Spooky, right? So, is there some identity to do with the inverse hyperbolic functions that I'm missing out on here, or is it just pure coincidence? Edit: wait, never mind, I'll try and derive something from the logarithmic form of sinh-1(x) No more edits: Done, thanks again for the help

Yep, I'm just getting on with it now, I've used a substitution of x=(2/√5)sinh(u), and I'm hoping it'll integrate to an inverse hyperbolic function, which is where the ln will come from? Edit: One of my new limits is sinh-1(2/√5), I hope I'm doing this right, haha... I like edits: Successful integration! Now it's just plugging the values of my limits in and tidying up, thanks for the help

There isn't an 'a', and it's a show that question so I know that's what it should come out as. I know their exponential forms, a few identities, and differentiation of their inverse functions / integration to their inverse functions Edit: hold on, I think some of the first part might be useful here, I'll put it in my first post Yet another edit: Never mind, there shouldn't be an a there, I've been really dumb... In the first part I differentiated some function sinh-1(x/a), but in this part a=1.... *facepalm self* Edits for days: right, I've chaged the first post and I'll try doing it without the 'a' complicating things now...

I still have no idea how I'm supposed to get the 1/8(12 + 5ln5) from that, or how to even choose a value for b.

Okay, so I've got a bunch of questions to do with hyperbolic functions, arc lengths and surface areas of revolution. I'm stuck on the final question, it's an integration that I have no idea how to even start... I know the arc length as an integral, but I'm having trouble actually integrating it... My y' was 2√(a2 + x2), which is definitely correct as the first part of the question was to show that. So in this next part, a = 1, so... L = (integral) [ √(5 + 4x2) ] The limits are 1 and 0, but I don't even know how to integrate this indefinitely, never mind definitely... So... Help? Edit: I've used Wolfram Alpha's integral calculator tool to find out what this integrates to, but still have no idea how to get there... Further edit: The value of L is supposed to be 1/8(12 + 5ln5)

I think some money was donated to charity instead. That's what people in the stream kasper posted said.

Woot woot!

As for why I'm excited right now, it's because harvester, dan and c7 are all online. This has to mean it's coming very soon

That ^ I'm hoping/expecting it to be released any time from now to a couple of weeks time.

Grats man, I remember the feeling of first landing on the mun!