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    Number of independent subcubes of a hypercube

    Number of "independent" subcubes of a hypercube Hello, I am trying to solve this problem: I have an n-dimensional hypercube and m of its vertices. Now I want to compute the maximum number of subcubes of the entire hypercube such that: - each subcube from the set may contain only those m...
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    Reproduction issue

    Why not? I can, indeed, end up with exponentially many organisms (exponentially many in n) - that was my concern. Is it really so obvious even if we take into account the limitation that each organism can reproduce only with polynomial (in n) amount of other organisms?
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    Reproduction issue

    I see. The universe (total population) is fixed and of the same size the whole time. It's only the subset which is growing.
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    Reproduction issue

    As I'm thinking about it again, now it seems clear to me that yes, we can end up with exponentially many organisms. I'm not sure what you mean for time to flow "independently of n", but we can imagine that time "happens" in discrete moments and only one thing can happen in each moment: two...
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    Reproduction issue

    Hello, let's have this scenario. We have a parameter n and a exponentially large (in n) universe of organisms. We are given a subset of this universe, which is only polynomially large. The only action which the organisms are able to do is that two compatible organisms join together and a new...
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    Is this sum exponential?

    Hello, I've been solving a problem which forces me to answer the question: "Is there a boolean function with exponential number (in variable count) of prime implicants of the length n - 1?" Anyway, during solving this problem I came to this point: Is the following sum exponential in 2n...
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    What is canonical and prime DNF?

    Hello, I'm little confused about canonical and prime DNF. I found on web that prime DNF is DNF consisting of exactly the set of the prime implicants. In school we've been told that canonical DNF is set of all prime implicants, so it gives me that prime DNF = canonical DNF. Then we...
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    Linear regression

    Homework Statement Consider model of linear regression: Y_i = \beta_0 + x_i \beta_1 + \epsilon_i i = 1, ..., 5, where \epsilon_i \sim \mathcal{N}(0, \sigma^2) are independent. Find expected value and variance of predicted values \widehat{Y}_i considering that observations are...
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    Confidence interval

    Let's say we know this: \sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right) How do we get from this information to this expression of confidence interval for \theta? \left( \widehat{\theta} \pm...
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    Estimation of parameters using maximum likelihood method

    Homework Statement Let's have random value X defined by its density function: f(x; \beta) = \beta^2x \mbox{e}^{-\beta x} where \beta > 0 for x > 0 and f(x) = 0 otherwise. Expected value of X is EX = \frac{2}{\beta} and variance is \mbox{var } X = \frac{2}{\beta^2}. Next...
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    Recursively enumerable predicate

    Hi all, could someone please explain to me, why, having recursively enumerable predicate Q(x,y) which is not recursive, the function defined as f(x) \simeq \mu_{y} Q(x,y) doesn't define partially recursive function? Ok, here's the argument for it: the program will "try" if Q(x,y)...
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    Computing axis forces of a construction

    Thank you very much, Cyclovenom! However, I'm still not able to finish the exercise. Could you please advise me which of the bars are zero-force? (I mean they have a zero axis force). Thank you in advance.
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    Equivalent characterization of uniform convergence

    Hi all, I'm learning some calculus theory and I found one point I don't fully understand: \mbox{Let M} \subset \mathbb{R} \mbox{ be non-empty set and let } f, f_{n}, n \in \mathbb{N} \mbox{ be functions defined on M. Then the following is true:} f_n \rightrightarrows f \mbox{ on...
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    Computing axis forces of a construction

    Hi all, I'm trying to compute the axis forces in the construction I put to attachment. I already have computed the R forces, but I don't know where should I start computing the axis forces from, from which point. Could please someone give me some advice? Thank you very much, best regards.
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    Little bit of statistics

    Thank you cepheid! That will be the one I'm looking for.
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    Little bit of statistics

    Homework Statement The bank is opened from 9:00 to 17:00. From 9:00 to 10:30 the average client count who come into bank is 32/hour, from 10:30 to 15:30 it is 26/hour and from 15:30 to 17:00 it is 50 clients per hour. I have to test the hypothesis that the average count of clients who...
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    Is this inequality correct?

    I've encountered this nice-looking inequality: \left(A+B\right)^{p} \le p\left(A^{p}+B^{p}\right) (p can irrational as well) but I can't find a way to prove or disprove its correctness. I've tried using the binomial theorem, but it didn't seem it would lead me to the finish...
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    Expected value of number of carps pool

    Maybe, but it seems rather obscure to me, I think they expect some kind of EX = ..., ie. expected value based only on current number of carps drawn out and the probability of drawing the marked carp in one individual step. When we were discussing this problem on our school forum, one of the...
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    Expected value of number of carps pool

    I still get the estimation for k: k = \frac{m.n}{x} where n is number of carps I have fished out so far and x is count of marked ones among them, so this expression gives me estimation of total carps count in n-th step. But I guess this is not what I was asked for in the original...
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    Expected value of number of carps pool

    Now I draw it, but I still don't know...In the beginning, I have m carps marked in the pool. I draw one. Probability that it will be the marked one is \frac{m}{m+u} where u is unknown and it denotes the number of unmarked carps in the pool. But I still can't figure out how can I conclude or...
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    Expected value of number of carps pool

    Homework Statement There is k carps in the pool, m of them are marked. I randomly fish out n carps and see that x of them are marked. What is the expected value of number of carps in the pool? (ie. expected value of number of the carps in the pool in the beginning) How will the...
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    Women and men around the table probability question

    No problem, it's always better for me to see there are more ways how to look at the problem (in case it's the correct answer, of course :smile: ) Thank you very much for your help!
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    Women and men around the table probability question

    So the final probability will be \frac{2n!n!}{(2n)!} = \frac{2}{\left( \begin{array}{cc} 2n \\n\end{array} \right)} ?
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    Women and men around the table probability question

    Ok Dick, for (i) I think it's (2n)! and for (ii) I'd say it will be n!.n!. Is it ok? But I don't know how to use or relate these two numbers, could you tell me a hint?
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    Women and men around the table probability question

    Is the probability \frac{2}{\left( \begin{array}{cc} 2n \\n\end{array} \right)} ?
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    Women and men around the table probability question

    Yes, I understand. I don't know how to prove it rigorously, but I guess every string really correspond to the same number of arrangements.. You're right, I didn't notice that. But what will be the total amount of strings then? As I think about it, could it be \left( \begin{array}{cc}...
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    Women and men around the table probability question

    Homework Statement Let's have 2n persons, n men and n women. Suppose they sit randomly around a table with 2n chairs. What is the probability that no two persons of the same sex will sit next to each other? The Attempt at a Solution Here's my idea: I will model this situation with...
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    Probability problem

    Thank you DH, now it's much more clear to me :smile:
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    Probability problem

    I'm little confused, why shouldn't I distinguish between those two 10-points shots? Ok, if I won't distinguish between them, then I will have 3 ways of ordering the shots. And, is there any simple answer to WHY do I have to take the order of the shots into account? I just can't see it...
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