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) =...