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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. ### Interpreting an Answer to Graph Structure Function

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) =...
25. ### A Level mechanics: Force exerted on a car by a trailer when brakes are applied

Thank-you so much for your help, Jay :) I understand this problem now. My exams in a few hours, so here's hoping that I'll do well :) Basically it came down to: F - 420 - (600g*sinA) = Mass x Deceleration F = 3720N
26. ### Help Needed: Self-Studying for A Level Mechanics 2 Exam

Inky, that gives me -9.9311, which is even further off from the book's answer :( Jay, I hope you're right :) Thank-you everyone for trying to help :)

28. ### A Level mechanics: Force exerted on a car by a trailer when brakes are applied

Jay, is this diagram okay? How do I apply Newton's second law of motion to this? From the diagram, I know that the resultant of all the forces [i.e. 11,500N + 420N - F - (600g*sinA)] causes the trailer to decelerate at 6.2ms^-2 down the incline. I'm really confused :S
29. ### 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...
30. ### Help Needed: Self-Studying for A Level Mechanics 2 Exam

Americanforest, based on the info you've given me, I've made some additions to my diagram. So will I now be taking the moment of the pink force (vertical component of the blue 5N force) about the point P? Pink force = 5N x sin 3.137 degrees Moment = CP x (5N x sin 3.137 degrees) = 0.528 Nm...
31. ### Help Needed: Self-Studying for A Level Mechanics 2 Exam

Americanforest, how does the force being applied at point C have an effect on P? The diagram is confusing me quite a bit. The fact that the triangle is a wire frame just confuses me further -- which forces act on P and which don't?. I'm not very good at mechanics, and I'm self-studying too, so...
32. ### Help Needed: Self-Studying for A Level Mechanics 2 Exam

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...
33. ### Help Needed: Solving Kinematics Problem in 10 Days!

Thank-you so much for your hints RoyalCat :) My answer finally matches the book's one: Position vector of Q = Integrating the velocity of Q = (-8t + a)i + [(3/2)t^2 + b]j As P and Q collide when t = 4, the position vector of Q = position vector of P at that time Hence, position...
34. ### Help Needed: Solving Kinematics Problem in 10 Days!

Hi RoyalCat :) Thank-you for your help. I'm guessing my book is wrong, unless someone else shows us otherwise? :) I've finally come up with something for part B. My answer of (24i - 32j)m for the position vector of Q with respect to O when t=0 doesn't match the book's answer of (24i - 8j)m...
35. ### Help Needed: Solving Kinematics Problem in 10 Days!

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...
36. ### 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...
37. ### Is magnetism more concentrated at the more pointed pole?

Diagram charge distribution on a similarly-shaped conductor:
38. ### 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...
39. ### Can someone suggest good websites for A Level (Grade 11 & 12) physics?

Thanks for your help! I have a copy of Halliday and Resnick but one of my teachers said that it was too complicated for my level and that it'd be easy to get derailed. But now I think I'll give it a shot!
40. ### 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...
41. ### Pressure Law - question about experiment apparatus

Thank you for your help and input. :smile:
42. ### 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)...
43. ### Basic optics (GCSEs in 3 days, )

Oh, thank-you for pointing that out! :redface: I understand it now. Thanks for your help and time everyone!
44. ### Basic optics (GCSEs in 3 days, )

Would it be logical to assume that all the light rays are horizontal? That's what I first thought, but the website said otherwise. It said that light striking the planar surface wasn't refracted. Maybe the writer was simplifying because the difference is so little?
45. ### Basic optics (GCSEs in 3 days, )

I know that incident rays arriving first at the planar surface aren't refracted because they strike the glass at 90 degrees (along the normal). I found that diagram as an applet on this site (which is about chromatic aberrations)...
46. ### Basic optics (GCSEs in 3 days, )

[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...
47. ### 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?
48. ### Comparison of sound waves in air and underwater

Ah, yes... it's a half-open tube. I keep getting my physics vocabulary mixed up. When you said open-ended tube I suppose you meant that the ear canal was actually open at one end but I misunderstood thinking you meant it was open at both ends. On this vein, do all sound waves strike the...
49. ### Comparison of sound waves in air and underwater

I'm still a little confused. If the ear is a closed tube and we apply the formula as such (wavelength = 4 x length of ear canal), then do all sound waves strike it at a node or do some (with a different wavelength) strike it at antinodes? I suppose if some did strike it at an antinode then the...
50. ### Comparison of sound waves in air and underwater

Speed in air = 0.1m x 3300Hz = 330m/s Using your equation: Frequency = v/(2L) = (330m/s)/(2x 0.025m) = 6600Hz It doesn't match the frequency provided by the question. :frown: L is the length of the auditory canal, right? And even if I used wavelength as L, it wouldn't match: Frequency =...