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Re: Statistics I computed an MGF to be m_X(u) = \frac{2}{u\theta^2} \left(\theta e^{u\theta}+\frac{1-e^{u\theta}}u\right) Therefore it does not exist because it's not defined for any u in [interval containing 0] right?

Re: Statistics Got it, thanks, 90% sure that was my confusion

Re: Statistics U1, ..., Un are iid Unif(0,1) Y_n := n \min\{U_1,\dots,U_n\}\\ \text{RTP: }F_{Y_n}(y) = 1-\left(1-\frac{y}{n}\right)^n So I followed their working up to F_{Y_n}(y) = \dots = \mathbb{P}\left(U_1\le \frac{y}{n}, \dots, U_n \le \frac{y}{n}\right) \text{But then for some reason...

Re: Statistics X_1, X_2 \sim \text{exp}(2)\text{ are iid.} And we're using the convention X ~ exp(a) => fX(x) = 1/a exp(-x/a) \text{Determined in part a) }f_{X_1,X_2}(x_1,x_2)=\frac{1}{4}e^{-\frac{x_1+x_2}2}\text{ for }x_1>0, x_2>0 \text{Define }Y_1 := \frac12 (X_1-X_2)\text{ and }Y_2:=X_2\\...

I feel that ACTL1101 just requires you to be extremely capable at handling algebra and also notation. Now that I'm in second year though things such as Newton's Method have appeared and there's a lot more proof based questions as well. Not everything you learnt in 3/4U is supposed to be the...

Re: MATH1131 help thread For starters The IVT is related to f The MVT is related to f' Whilst obvious, this saved me a bit of thinking a few times. Perhaps more clearly, very rarely do you ever use the MVT to show the existence of the root. The IVT wants you to examine the actual function...

Re: MATH1131 help thread Yes, you do need to find an interval to use the IVT for [R]. But since the question just specifies that at least one root must exist, nobody is going to care what interval you pick. You just have to pick any interval that works. [H] is different because you're...

Re: MATH1131 help thread Reasons that are similar to how IG gets out all of my questions so quickly

Re: MATH1131 help thread \text{Fix }x> 0\text{ and let }f(t) = \sqrt{1+t}\implies f^\prime(t) = \frac{1}{2\sqrt{1+t}} \\ \text{Since }f\text{ is continuous on }[0,x]\text{ and differentiable on }(0,x)\\ \text{By the MVT there is a }c\in (0,x)\text{ such that}\\ f^\prime(c) =...

I know. RIP. It's like a pure maths trademark course. And I wanna do pure...

Re: MATH1131 help thread \text{Note that }f\text{ is continuous on }[1,3]\text{ and differentiable on }(1,3)\\ \text{so the MVT may be applied.} \text{By the MVT, there is a value of }c\in (1,3)\text{ such that}\\ f^\prime(c) = \frac{f(3)-f(1)}{3-1} \\\text{But note, by computation, that...

Basically as the title suggests. I don't really know who to ask (Shadowdude maybe?) so I'm just leaving this here. Does anyone have any insight on how difficult this course is and any tips to doing well in it?

Re: Statistics \text{This formula you're just gonna have to know. Because in our courses we only consider (at most) bivariate distributions}\\ \text{I'll just assume that the other r.v. is }X f_Y(y) = \int_{\mathbb{R}} f_{X,Y}(x,y)\,dx\text{ for continuous} \mathbb{P}(Y=y) = \sum_{\forall...

Re: Statistics Ouch. Thanks, overlooked that completely. So I should always use the substitution method when they aren't independent?

Re: Statistics \text{Given }f_{X,Y}(x,y)=2(1+x+y)^{-3}, \, x,y >0\\ \text{find the density function of }X+Y \text{The solutions presented the method of letting }U=X+Y\text{ and }V=Y\\ \text{which resulted in }f_{U,V}(u,v)=2(1+u)^{-3}\\ \text{and then they just found the marginal density...

Re: Statistics The content isn't really examinable but it was taught anyway, so I want to grasp some of the intuition behind it for future reference. What would be some examples of convergence almost surely and convergence in probability? And with or without the mathematical definition, how is...

Do CompSc then yeah Well, I'm also a bit passive about Actl. I still do it anyway though; the things I learn in it are pretty cool. Only ditch it if you think it's a waste of both time and money I suppose. Not really. Interest maybe maths but career I wouldn't have a clue tbh (Wow ok stalker :P)

Not true. The locus is only the arc of a circle, not the entire circle.

Re: UNSW chit chat thread 2017 How sadistic am I if I feel like overloading again...

Nah I feel you. I have no clue if actuarial is right for me either. Coding is fun. If you like it then you should definitely pick up computer science (or SENG if you prefer that). Schools not offering technology based subjects shouldn't impact that at all. One of the many reasons why I do two...