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  1. S

    Can a preference relation be complete but not transitive?

    No worries, I have figured this problem out. Please close this thread.
  2. S

    Can a preference relation be complete but not transitive?

    Please move this thread if it is more appropriate for the 'General Math' forum (https://www.physicsforums.com/forumdisplay.php?f=73). Thank you.
  3. S

    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

    Thank you both for your answers. I was really confused by the poor wording of the document, but I think I understand what my professor is trying to say. :)
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    Expected return for n = ∞, normally dist. assets, portfolio theory

    Thank you for your reply Bruce. If we break down 100(1+\bar{R}) into its components, we have 100 + 100\bar{R}. Is my professor trying to say that this is the final accumulation that I end up with? That is, i) I will have my original $100. ii) on top of that, I will have returns that should...
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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?

    Thank you for all of your help Ray. I really appreciate it. All that I've managed to gather is that the expected value of the error term is zero, the expected value of the error term conditional on X is zero, that the variance of the error term is constant for all the values of the independent...
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    Is the estimator for regression through the origin consistent?

    We assume that the error terms (u_i) follow a normal distribution. Hence, in a sufficiently large sample (as n approaches infinity), the sum of the errors should converge to 0. Hence,Ʃx_iu_i = 0. Are there other assumptions we have to make?
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    Is the estimator for regression through the origin consistent?

    I just realized that there are no \hat{u_i}, since regression through the origin means that there cannot be any sample-level error variables. Hence these are missing from the formula I derived in part (a). According to Wikipedia, "The error is a random variable with a mean of zero conditional on...
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    Is the estimator for regression through the origin consistent?

    Sorry, I forgot to add the subscript for the u_i. I might not have explicitly mentioned this before, but I am deriving the OLS estimator for regression through the origin. \tilde{\beta_1} = \frac{\sum_{i=1}^{n}x_i(\beta_1x_i + u_i)}{\sum_{i=1}^{n}x_i^2} = \frac{\sum_{i=1}^{n}\beta_1x_i^2 +...
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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

    Thank you for your suggestions Ray and HallsofIvy. From what you're saying, I understand the following: 1) The probability that the point lies within the circle is 1. 2) We want to find the probability that the point lies within a distance d of the circle's center, where 0 ≤ d ≤ 1. Hence I...
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    Probability that distance from the origin of a uniformly distributed point < x

    \pi(r^{2}). I'm not sure how this relates to the question, since I don't understand how D can ever be less than x for a given value of x (unless I'm understanding this incorrectly).
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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?

    jbunniii and Ray, thank you again for all of your help! I understand the proof now.
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    Why is E(X^3) = E(X) = 0, if X is symmetrically distributed about 0?

    f(0) = 0 for any odd function because the only number that does not change when it is multiplied by -1 is 0: f(-x) = -f(x) f(-0) = -f(0) f(0) = - f(0) Since f is an odd function, \sum_{n = -\infty}^{-1} f(n) = \sum_{n = 1}^{\infty}f(n) Hence, \sum_{n = -\infty}^{\infty} f(n) =...
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    Why is E(X^3) = E(X) = 0, if X is symmetrically distributed about 0?

    Thank you for the clarification. Let the constraint be that E[X] and E[X^3] exist for X, which is a symmetric (center 0) discrete RV. I don't know any more information about the specifics of the distribution. The product of an odd and an even function is an odd function. Hence, E[X] is an odd...
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    Why is E(X^3) = E(X) = 0, if X is symmetrically distributed about 0?

    Thank you again for your help. I'm sorry if my questions are really basic. I just started learning about basic probability and statistics, so I'm a bit weak on general concepts and proofs. Thank you for clarifying this. I'm not trying to prove this for a specific probability distribution...
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    Why is E(X^3) = E(X) = 0, if X is symmetrically distributed about 0?

    Thank you for your help! I'm still a little confused about some things, which I'll go through. p(n) is an even function since probabilities are positive. Would it be possible for me to derive E(X^3) = E(X) = 0 without using the summation formula you noted? Does the simple example that I...
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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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