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)...
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...
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. :)
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...
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...
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...
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?
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...
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 +...
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...
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...
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...
\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).
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...
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...
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) =...
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...
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...
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...
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) =...
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
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
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...
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...
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...
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...
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...
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...
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...
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...
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...
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!
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...
[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)...
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?
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)...
[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...
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?
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...
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...
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
=...