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  1. B

    Basic probability exercise

    :-) Precisely. Hopes somebody weighs in...
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    Basic probability exercise

    Hmm. In (a) there are two ways of getting all assignments wrong (if the correct one is 123, then these are 312 and 231) and there are 3*2*1 = 6 possible assignments. If his guesses are random this yields Pr(all wrong) = 2/6 = 1/3. In (b) I count 9 ways of getting all assignments wrong out of...
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    Basic probability exercise

    Yeah, I think I'll do that, although it gets rather complex in (b). A slight problem though: when I count the combinations I get 3/8 in (b), but when I calculate it using the multiplication rule I get 1/4 :eek:
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    Basic probability exercise

    Hi. I'm a math instructor and this problem is given to 1. year economics students. 1. The problem statement In an episode of the TV show "All in the Family", Mike claimed that he could identify different brands of cola by taste alone. He was challenged and presented with three glasses, one...
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    Conditional distribution

    I've been staring at this for hours. Any hints? Let the vector Y = (Y_1,Y_2,\dots,Y_k) have a multinomial distribution with parameters n and \pi = (\pi_1,\pi_2,\dots,\pi_k): \sum_{i=1}^{k}Y_i = n, \quad \sum_{i=1}^{k}\pi_i = 1 Show that the conditional distribution of Y_1 given...
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    Optical isomerism

    It's in the context of simple http://wwwchem.uwimona.edu.jm:1104/courses/CFT.html". I don't think there's any unobivious rules here, but I don't know...
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    Optical isomerism

    I see your point. If we assume that every H2O molecule occupies one ligand space and does not interact with it's neighbors -- would I then be correct? It's an introductory course, so I assume there's no pitfalls.
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    Optical isomerism

    Hi. I'm asked the following question: What isomers does the complex [\text{Fe}(\text{H}_2\text{O})_6] give rise to? Is it optically active? My answer to the first question would be 'none': The 6 identical H2O molecules are arranged in an octahedral fashion around the central Fe-atom, so...
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    Bonding etc.

    c) Still in the dark. Can't relate these things to the activation energy... sorry. f) Oxygen is more electronegative than nitrogen, so the OH-molecule has a greater dipole strength than the NH-molecule and therefore the hydrogen bond is stronger in the former case (O-H---O). Right? Thanks...
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    Bonding etc.

    Hi. I need help with (part of) this exercise: c) By considering the differences in bonding determine which of the combustion reactions (in part a) I have written combustion reactions for the following hydrides: B2H6, CH4, NH3 and H2S) must be expected to have the lowest energy of activation...
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    Solubility problem

    Hmm, not sure. But I think I know how to do it now. Thanks.
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    Solubility problem

    It will shift to the right, so the solubility will go up (consistent with my result.) I should compute the I3- concentration and add it to the I2(aq) concentration to find the new solubility, right?
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    Solubility problem

    Hi. I'm preparing for a chemistry exam and I have trouble with this former exam problem: The solubility of I_2\text{(s)} in water at 25ºC is 0.0013 M. Calculate the solubility of I_2\text{(s)} in a 0.1 M solution of KI(aq) by considering this equilibrium: I_2\text{(aq)}+I^-\text{(aq)}...
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    Enthalpy of hydration

    I have no idea, just quoting from the book, basically. Doesn't Li- and Cs-solids exist? I'm a lousy chemist, I know. I would think that "quietly" means slow and "violently" means fast, so the statement is that the reaction rate of Cs + water is larger than the reaction rate of Li + water. I...
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    Enthalpy of hydration

    The Li atoms are smaller, but how does that affect the reaction?
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    Enthalpy of hydration

    Hi. How come that Cs reacts more violently with water than Li, when the enthalpy of hydration for Li is -520 kJ/mol while it is only -276 kJ/mol for Cs. More energy is released in the Li reaction, but still it reacts more quietly? (EDIT: Oops, maybe this should be in the homework section?)
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    Single particle states?

    And yet another thing: even though the electrons doesn't interact, they still have to obey the Pauli exclusion principle, right? So we can't consider them independently after all, or...?
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    Single particle states?

    I see. Thanks. Oh, just one more thing: how do you construct the state vector for the whole system from the individual single particle states? Is it like a tensor product (I'm unsure of the mathematics here.)
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    Single particle states?

    Hi, I was just reading up on some QM, and I was wondering this: under what circumstances can you treat a bunch of electrons as occupying "single particle states", and when do you have to use one wavefunction depending on all the coordinates, psi(r1, r2, r3, ...)? Hope you know what I mean...
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    Why 'axioms'?

    Thanks, I think I'll pick that one up.
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    Why 'axioms'?

    By the way, does anybody know of a good, relatively accessible, introduction to the subject of mathematical logic?
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    Why 'axioms'?

    Oh, I think I get it now. I guess I was confused about the distinction between the axioms themselves and 'the model' to which they are applied. Thanks, everyone.
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    Why 'axioms'?

    But you can't prove an axiom, and 1-4 can be proved (or disproved) for a given set?
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    Why 'axioms'?

    Hi. I'm reading a simple introduction to groups. A group is said to be a set satisfying the following axioms (called the 'group axioms'): 1) Associativity. 2) There is a neutral element. 3) Every element has an inverse element. 4) Closure. My questions is simply: why are they...
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    Spin-up effect?

    Hi. Can anyone explain to me what spin-up effects are? The context is a waterwheel that consists of an ordinary wheel with papercups with holes in the bottom suspended along the rim. It is stated that for this wheel there are two sources of damping: ordinary frictional damping and "inertial"...
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    Dimension of fractal object

    I'll try to locate that one. Thank you!
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    Dimension of fractal object

    Hi. How can I "experimentally" (by way of computer simulation) calculate an approximate value for the dimension of a fractal object? The object in question is the Lorenz strange attractor, which has a dimension between 2 and 3. Also, I know there is a number of different ways to define...
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    Sensitive dependence on initial conditions

    No, obviously I don't :biggrin: I'll take a look at it, though. Thanks!
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    Sensitive dependence on initial conditions

    Yes, that seems plausible, but is it always possible? One could imagine that it would be practically impossible if the sensitivity is critical enough. It usually isn't, I guess, since no one seems to care about it. It just seems like a problem as significant as the problem of the precise...
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    Sensitive dependence on initial conditions

    Hi. I'm starting a project on chaos very soon and I was just wondering... One of the distinguishing features of a "chaotic system" is the sensitive dependence on initial conditions. It is stated that if we knew the initial conditions with infinite precision we would also be able to...
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