Recent content by rahl___

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    [markov chain] reading expected value from the transition matrix

    Hello there, yet another trivial problem: I've attended the 'stochastic process' course some time ago but the only thing I remember is that this kind of problem is really easy to compute, there is some simple pattern for this I presume. thanks for your help, rahl.
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    [probability theory] simple question about conditional probability

    Hi all, I've got this very simple problem: I know it is an elementary problem, but I never really got into that bayes' theorem, which I need to use here, right? I would be grateful for simple and plain explanation. thanks for your time, rahl.
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    Solve log(base4)X + log(base4) (X+6) <2

    this property should be useful: log_a (b*c) = log_a b + log_a c applying this to your inequality and changing 2 into log_4 16 you'll get something that can be easily transferred into inequality containing quadratic function, which you'll surely solve on your own
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    [measure theory] measurable function f and simple function g

    Hi everyone! my problem: since every simple function is bounded, we at once know, that either is our function f, cause: - \epsilon + g(x) <= f(x) <= \epsilon + g(x), so that's obviously not the problem here. this whole measure stuff doesn't get into my intuition and I don't have any...
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    [complex functions] polynomial roots in a convex hull

    I have found the solution. If no one deletes this thread, I will write how to solve it, maybe it will help someone some day.
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    [complex functions] finding complex roots in 1+z+az^n

    of course they dont, I don't know what I was thinking when writing that. I don't understand what you are implying. Let z=4 and a = \frac{-5}{4^n}. In that case |W(4)|=0, so there obviously is a solution outside that circle. EDIT: I have googled a hint...
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    [complex functions] finding complex roots in 1+z+az^n

    Hi, I have a big problem in solving such question: I have no ideas how to solve it. I thought about integrating W and showing that it's roots create a circle with radius equal to 2, but it completely didnt work. I would appreciate if someone could give me a clue, as I really can't see any...
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    How can I solve the following equation

    Hi, I doubt whether this is the sollution you wanted to see, but this kind of equations are usually solved numerically [please correct me if I am wrong]. My proposition: we have a function: f(x) = 2^x + 6x - 2^4 three facts that are obvious: the function is continuous and strictly...
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    [complex functions] polynomial roots in a convex hull

    Hi everyone, I've got this problem to solve: My problem is that I don't fully understand the question. I have found such definition of convex hull: So I do have to prove, that all the roots of W'(z) [let's denote them as z'_k] must be able to be written in such form: z'_k = \sum_{k=1}^n...
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    [optics] reflection and refraction

    i have a problem with understanding the phenomenon of reflection and refraction of light. when considering light as a electromagnetic wave i cannot imagine how it can be reflected or refracted when meeting a surface of different refractive index. it just sounds illogical to me that sth...
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