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  1. C

    How to make matrix positive definite (when it is not)?

    I was hoping to "make" it positive using some trick, but after looking around again I am wrong. Like you said, if it's NOT positive definite, then it's not. I also realized there's an error when putting together the matrix. So, problem solved I guess.
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    How to make matrix positive definite (when it is not)?

    Suppose I have a matrix that looks like this [,1] [,2] [1,] 2.415212e-09 9.748863e-10 [2,] -2.415212e-09 5.029136e-10 How do I make it positive definite? I am not looking for specific numerical value answer, but a general approach to this problem. I have heard...
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    What is copulas exactly, in probability and finance terms

    I am not using R, but even in R there's an algorithm right? Is there a way to see what they did in the package?
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    What is copulas exactly, in probability and finance terms

    Thank you zlin034. What do you use to simulate copulas, Gaussian and student-t? I have two ideas for bivariate Gaussian: 1. integrate the density from Wiki, here http://en.wikipedia.org/wiki/Copula_(probability_theory)#Gaussian_copula or this...
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    What is copulas exactly, in probability and finance terms

    Hi, all I have been reading about copula, but still very confused. What exactly is a copula? My understanding is: there are couple of components 1. uniform cdf marginal 2. a covariance matrix What exactly is this thing? Why am I calculating the marginals and what does it have to do...
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    How to integrate x^(-a)*e^(-b/x), where a, b are constants?

    wow, you are really good. Yes, I wrote a simplified version of inverse-gamma. I am looking for the posterior distribution.
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    How to integrate x^(-a)*e^(-b/x), where a, b are constants?

    Homework Statement How do you integrate this? x-ae-b/x, where a and b are some constants. The Attempt at a Solution I have tried this http://integrals.wolfram.com/index.jsp?expr=x+*+e^%28-1%2Fx%29&random=false Is there a closed form of this?
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    What kind of test should I use for before and after treatment

    I was wondering about this, since the researcher himself said "binomial distribution z statistics with continuity correction." Also, he said "The P values were calculated by comparing the observed proportion based on 29 patients..." I am just thinking...what in the world?! why? The article...
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    What kind of test should I use for before and after treatment

    thanks! :) So, why am I told to use normal approximation to the binomial. I understand the normal part, but not the binomial part, where that does binomial come from? Here is another site that actually explains it, but I am still confused...
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    What kind of test should I use for before and after treatment

    What test or distribution should I use for before and after treatment? Say, I have 30 subjects I test their blood before and after a pill they take a pill, what kind of test should I use? I want to test mean difference, so, paired t-test? or Wilcoxon signed rank test? The data looks like this...
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    Proof for upper bounded sets

    Why is limit point called a limit point? does it have to do with limits? I know if you talk intervals on a real line in 1-d, you can talk convergence. But when we talk about 2-d, like open balls, why are we calling it limit point, even the definition of a limit point does not mention anything...
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    Proof for upper bounded sets

    hey, Fredrik. I figured it out. Yes, this is the ultrametric space. Thanks, just wanted to know I am thinking right. For the standard metric. If I have a closed ball, is the interior point same the limit point? I mean the definition of interior point is, open ball B(x,r) is contained in...
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    Proof for upper bounded sets

    thanks a lot, Deveno. To prove an open ball B(x,r) is also closed. Is it ok to start like this? Let p be a limit point of B(x,r). If p\notinB(x,r), then, p\inB^{c}(x,r). Where I said "let p be a limit point of B(x,r)." I though limit point only existed in closed balls, but B(x,r)...
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    Proof for upper bounded sets

    wow, that was such a long post. When you say an open set is a union of open balls. How do you actually write that in proof? For all x \in X, there is a ε>0, such that B(x,r) is completely contained in E. Does this look good?
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    Proof for upper bounded sets

    yessss, that makes sense to me. What exactly is an open set, what is its role in all this? I have read it in Rudin and Wiki. It's saying... say, we are in some space E, we have a point y≠x such that d(x,y)<ε. Another way is to say that every open ball B(x,ε) is completely contained in E...
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    Proof for upper bounded sets

    Yes, I see what you are saying, so when I say an open set, I have to refer back to X, so the reader won't confused thinking that it is in B? But isn't open in B the same thing as open in X, since B\subsetX. I mean, they are kind of different since X is bigger than B. But open in B is also...
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    Proof for upper bounded sets

    I think I got it, it was that bad actually. Could anyone help me with this? If B and B' are subsets of X, A\subsetB, and A\subsetB', then A is open in B\cupB'. The proof is started, but I don't understand what it is saying A is open in B implies A = O_{B}\capB for some open set O_{B} in...
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    Proof for upper bounded sets

    thanks, this is just a hard question for me, let me follow your work and work it out see if it makes sense to me.
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    Proof for upper bounded sets

    Hey, Kreizhn. Sure. I don't understand why we need epsilon in the proof, seems like we never used it.
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    Proof for upper bounded sets

    Why do you have to even say epsilon>0? You never use epsilon besides attaching it to x. I see this somewhere else too, I am confused.
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    How is (0,1) not compact?

    I am confused. Seems like you can use (1/n, 1) to argue for (0,1) or [0,1] and say it is not compact. Because the subcover is infinite in (0,1) and [0,1].
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    Prove [0,1] is non-empty and bounded above

    great! I will get started, I am not sure if I will come back for more on this one. But one thing for sure, I am learning more on PF than in class.
  23. C

    Prove [0,1] is non-empty and bounded above

    Thanks again! I just feel like banging my head against the wall. Actually I want to bang Rudin's head against the wall. So, frustrating! Anyways, let \gamma=Sup E, how do you prove \gamma\inE. I know the definition of Sup, but how do you show something is a supremum?
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    Prove [0,1] is non-empty and bounded above

    thanks, micromass. :) So, I was right? I feel like Rudin is a little overated(no examples). How do I learn how to prove this? I know I am suppose to work hard, but you can't just beat me around the bush. Anywho, does anyone know some good websites? I've been look at other course websites...
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    Prove [0,1] is non-empty and bounded above

    Does anyone else know? someone is gotta know this, chapter 2 of Rudin. *patiently waiting*
  26. C

    Prove [0,1] is non-empty and bounded above

    I found t=0, there is only one element in that interval, namely {0}. What's wrong? Let me continue from earlier. [0,0]={0} \in[0,1] There exists some I_{\alpha} that covers {0}, and there is a finite number of open covers. So, E\neq\emptyset. Since E={t|t\in[0,1] and [0,t]...}...
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    Prove [0,1] is non-empty and bounded above

    Homework Statement Want to prove that [0,1] in R is compact. Let \bigcup_{\alpha\in A} I_{\alpha} be an open cover of [0,1]. By open sets in R. Let E={t\in[0,1] s.t. [0,t] is covered by a finite number of the open cover sets I_{\alpha}}. Prove that E\neq\emptyset. The Attempt at a...
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    Are interior points also limit points

    We use open ball to define both limit point and interior point. Say, we have some set of space, call it S. When point p is a limit point of S, we say that we can find a point q (q≠p) in B(x, r), meaning an open ball centered at x, with radius r. When it is interior point, we say all...
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    Are interior points also limit points

    Homework Statement Are interior points included in (or part of) limit points? Homework Equations Since the definition of interior points says that you can find a ball completely contained in the set. For limit points, it's less strict, you just have to find a point other than the center...
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    How to prove rational number is a commutative field

    Thanks so much, I think I got it, that was very helpful! :)
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