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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

    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?

    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

    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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    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

    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

    I was wondering how to prove rational number is a commutative field. Personally, I didn't think the word "commutative" is necessary, how about others? Do I simply prove it is commutative under multiplication?
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    Is group mean and overall mean independent?

    In an ANOVA experiment, you have, group mean \overline{y}. overall mean \overline{y}.. Are they independent? Some samples overlap to calculate these means. What is var(\overline{y}.-\overline{y}..) ?
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    Minimizing cost function Statistics

    Homework Statement Let X and Y be two unknown variables with E(Y)=\mu and EY2 < \infty. Homework Equations a. Show that the constant c that minimizes E(Y-c)2 is c=\mu. b. Deduce that the random variable f(X) that minimizes E[(Y-f(X))2|X] is f(X)= E[Y|X]. c. Deduce that the random variable...
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    Why is waiting time memoryless? (in Stochastic Processes)

    I am learning Stochastic Processes right now. Can someone some explain why waiting time is memoryless? Say, if a light bulb has been on for 10 hours, the probability that it will be on for another 5 is the same as the 1st 5 hours. It doesn't make sense to me, because the longer you use it...
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