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    Can a preference relation be complete but not transitive?

    Homework Statement This is not a homework problem, but a topic in a microeconomics book that I am unclear about. My book argues that the set X = {a, b, c, d} of preferences can be (i) transitive but (ii) incomplete. Is it possible for a similar set of preferences to be (i) complete but (ii)...
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    Least squares assumptions: finite and nonzero 4th moments

    This isn't a homework problem - I'm just confused by something in a textbook that I'm reading (not for a class, either). I'd appreciate an intuitive clarification, or a link to a good explanation (can't seem to find anything useful on Google or in my textbook). My book states that one of the...
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    Expected return for n = ∞, normally dist. assets, portfolio theory

    Homework Statement My economics exam is in a few days. My professor posted solutions to a sample final, and I'm confused by one of the answers. I won't have access to him before the exam, so I can't ask him to clarify. I'm hoping that someone here can help. ____ QUESTION: You have $100 at...
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    Is the estimator for regression through the origin consistent?

    Homework Statement Any help on this would be immensely appreciated! I am having trouble interpreting what my instructor is trying to say. Consider a simple linear regression model: y_i = \beta_0 + \beta_1x_i + u (a) In regression through the origin, the intercept is assumed to be equal to...
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    Simple structure function - interpreting answer [Probability & Reliability Theory]

    Homework Statement This isn't a homework question. I'm working through my book's exercises and am having difficulty interpreting an answer. Any guidance will be very much appreciated. The problem is to come up with a structure function for a graph (image attached with this post). The answer is...
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    Probability that distance from the origin of a uniformly distributed point < x

    Homework Statement A point is uniformly distributed within the disk of radius 1. That is, its density is f(x,y) = C For 0 ≤ x2 + y2 ≤ 1 Find the probability that its distance from the origin is less than x, 0 ≤ x ≤ 1. [Note] My book says that the answer is supposed to be x2. 2. The attempt...
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    Marginal probability & law of iterated expectations for three jointly distributed RVs

    Homework Statement Consider three random variables X, Y, and Z. Suppose that: Y takes on k values y_{1}.... y_{k} X takes on l values x_{1}.... x_{l} Z takes on m values z_{1}.... z_{m} The joint probability distribution of X, Y, and Z is Pr(X=x, Y=y, Z=z), and the conditional probability...
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    Why is E(X^3) = E(X) = 0, if X is symmetrically distributed about 0?

    This is not a homework problem but is rather something I'm curious about. I apologize if the answer is very simple, but I am having trouble coming up with an absolute and strict proof. * X is a discrete random variable that is symmetrically distributed about 0. Hence, E(X) = 0 * Why is E(X^3) =...
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    A Level mechanics: Force exerted on a car by a trailer when brakes are applied

    Hi :) I have an A Level Mechanics 2 exam in 3 days. I managed to 'solve' this problem from my book, but I'm having some trouble with the underlying concepts. It would be really nice if someone could explain part (c) of the question to me (I've included my solution below but I don't understand...
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    Statics of rigid bodies – calculating the moments about a point. A Lvl exam in 4 days

    Hi :) I’m self-studying for my A Level mechanics 2 exam (it’s in 4 days :S) and there’s a problem in my book that I just can’t solve. Any help would be really appreciated. :) Homework Statement Find the sum of the moments about the point P of the forces shown in the diagram...
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    A Level Mechanics: Kinematics of 2 particles moving in the same plane [i, j vectors]

    Hello :) I'm self-studying for my Edexcel Mechanics 2 GCE A Level exam (it's in 10 days :S) and was having lots of trouble with one of the kinematics questions. I've uploaded photos of the problem and my solution for part (a) of the question. I couldn't use the math notation feature on the...
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    Intensity-wavelength graph for emission spectra; why is frequency in the x-axis?

    In my astrophysics book (Astrophysics, Nigel Ingham), there are intensity-wavelength graphs for line spectra (both emission & absorption). On the y-axis, relative intensity is plotted. But on the x-axis, frequency and not wavelength is plotted. Why is this? If I wanted to convert this graph to...
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    Is magnetism more concentrated at the more pointed pole?

    There's a principle that the electric field is stronger/more intense at the most pointed parts of a charged, non-uniform conductor. Does this principle also apply to magnets? I.e. if we have a non-uniform magnet, is the magnetism density (sorry for the lack of a more scientific word) greater...
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    Can someone suggest good websites for A Level (Grade 11 & 12) physics?

    Hi! I'm an A Level student studying under the British Edexcel specification (8540). I'm struggling with physics. My teachers at school are uncooperative and boring; it's only been a month and without reviewing basics they're already taking tests. I don't remember much from my GCSEs and my books...
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    Pressure Law - question about experiment apparatus

    [SOLVED] Pressure Law - question about experiment apparatus Introduction Above is a diagram representing the apparatus which can be used to perform the experiment which verifies the Pressure Law (i.e. pressure is directly proportional to temperature for a fixed mass and volume of gas)...
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    Basic optics (GCSEs in 3 days, please help)

    [SOLVED] Basic optics (GCSEs in 3 days, please help) Homework Statement Here is a diagram of light passing through the curved edge of a planoconvex lens. When a light ray strikes the planar edge, it is not refracted. Why? 2. The attempt at a solution The website the diagram came...
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    Why does a whistle sound louder when you blow harder?

    I've noticed that the harder you blow into a whistle, the louder the sound produced. Why is this? Does the high speed of the air rushing into the whistle increase its vibrational amplitude? Do compressions and rarefactions of the air have anything to do with it?
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    Comparison of sound waves in air and underwater

    [SOLVED] Comparison of sound waves in air and underwater Homework Statement In air, the human ear is most sensitive to sound waves of 3300Hz. The auditory canal is part of the human ear. It is a tube of length 0.025m, i.e. 1/4 the wavelength of sound with frequency 3300Hz. When under...
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    Voltage and Current

    [SOLVED] Voltage and Current Homework Statement A d.c. circuit has a 20ohm resistor and ammeter connected in series. A voltmeter is connected in parallel to the resistor. After some time, the reading on the ammeter suddenly decreases to nearly zero, but the voltmeter reading remains at 4V...
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    How is charge transmitted between two metal plates separated by air?

    My teacher marked my answers to this assignment as wrong. He wouldn't explain why, so I hope you guys will be kind enough to point me in the right way :smile: The reading of the sensitive ammeter was found to be 0.002mA. Radon-220 isotopes are introduced through the valve and it releases...
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    What's the formula for calculating large exponents?

    [SOLVED] What's the formula for calculating large exponents? Hi! I came across the following sum and was wondering if there was some kind of formula for solving it: 16^198 Is it some kind of binomial expansion? Do you calculate the last digits first, advancing to the previous ones later? I...
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    Vectors: air speed, ground speed

    [SOLVED] Vectors: air speed, ground speed I'm having trouble drawing the diagram for this question. Homework Statement An airplane with air speed 120 km/h is heading due north in a wind blowing due east at 50 km/h. What is the ground speed of the plane? Homework Equations Pythagoras...
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    How does charge move from the inside to the outside of the butterfly-net?

    Please can someone help me with this? Thanks in advance. :) Homework Statement 'No charge is present on the inside surface of a charged hollow conductor'. In Faraday's butterfly net experiment, when the positively charged net is turned inside out, the outside is still charged. How does the...
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