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1. Can a preference relation be complete but not transitive?

No worries, I have figured this problem out. Please close this thread.
2. 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. 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)...
4. Least squares assumptions: finite and nonzero 4th moments

Thank you so much!
5. 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...
6. 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. :)

9. 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...
10. 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?
11. 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...
12. 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 +...
13. 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...
14. 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...
15. 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...
16. 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).
17. 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...
18. 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...
19. 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.
20. 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) =...
21. 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...
22. 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...
23. 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...
24. 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) =...