Recent content by michonamona

  1. M

    A simple conditional expectation question

    Let v be a random variable distributed according to F(.). Let X be a set containing the objects x1 and x2. Suppose E(v|x1) = b AND E(v|x2) = b (The expected value of v conditional on x1 is b, etc) where b is some constant. Does it follow that E(v|x1,x2) = b? If so, why...
  2. M

    How do you graph this function?

    Homework Statement For a given fixed value, z, how would the level curves of the function below look like? (i.e. the graph of the function in the xy plane, for some given value z. z = min(2x+1, x+y, 2y+1) Homework Equations The Attempt at a Solution Ive been working on...
  3. M

    Given a discontinuos function, show that it is not concave

    Its called Microeconomic Theory by Mas-Collel, Winston, and Green. I thought concavity was a general mathematical property, I learned it in Real Analysis.
  4. M

    Given a discontinuos function, show that it is not concave

    I'm trying to show that if the function f is discontinuous, then it cannot be concave. Here's the general definition of concavity Let f be a function of many variables defined on the convex set S. Then f is concave on the set S if for all x ∈ S, all x' ∈ S, and all λ ∈ (0,1) we have...
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    Given a discontinuos function, show that it is not concave

    Hello, It's a class in Microeconomic Theory Thanks
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    Given a discontinuos function, show that it is not concave

    Homework Statement Let f be a function from (1,0) to (1,0). Suppose that f is discontinuous. Show that f is not concave. Homework Equations The Attempt at a Solution Let f:(0,1)-->(0,1). Suppose f is discontinous. Show that it is not concave. I've been working on this problem for over...
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    Traveling at Light Speed Through Space: A Thought Experiment

    Thanks everyone for your response. I'm an amateur in physics so could someone explain why it is not theoretically possible for a spaceship to travel at the speed of light? Does it have something to do with Einstein's E=mc^2? Also, does ".99c" stand for ".99 percent of the speed of light"...
  8. M

    Traveling at Light Speed Through Space: A Thought Experiment

    My brother-in-law proposed the following thought experiment: Suppose a person was sitting on the nose of a spaceship traveling at the speed of light through outer space. Now suppose that person pushed off against the spaceship launching himself ahead of it. Is it the case that that person will...
  9. M

    Modulo operation | What does this mean?

    Homework Statement Suppose i and j take on values from {0,1,2,...,7}. We say that i and j are 'happy' if i - j (their difference) is congruent to 1.4 or 7 modulo 8. Note: 'happy' is some mathematical property not relevant to the question. What does 7 modulo 8 mean? What does it...
  10. M

    Size of the Power Set

    Homework Statement Why is the size of the power set 2^n ? To elaborate, suppose we have a set B that has n elements. Let C be the set that contains all the possible subset of B. Why is it that |C|=2^n ? It boggles my mind why the base is 2 for all size of sets. Thank you, M...
  11. M

    Whats the derivative of the absolute value to the power of p?

    Ok, |x|^p is definitely continuous everywhere. I graphed it and it looks differentiable at x=0 (seems to be the local min). Is the following a valid proof? Show that |x|^p, p>1 is differentiable at x=0 lim_{h->0^{+}} \frac{|0+h|^{p} - |0|^p}{h}= lim_{h->0^{+}} \frac{|h|^{p}}{h}=lim_{h->0^{+}}...
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    Whats the derivative of the absolute value to the power of p?

    Homework Statement Let p>0. What is the derivative of |x|^{p}? Homework Equations The Attempt at a Solution I know that if p is even, then the derivative is just px^{p-1} . But what if x is odd? Would it turn out to be some piecewise function, such as px^{p-1},\: if x \geq 0 and...
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    Prove that the functin is differentiable at (0, ,0).

    You mean using: lim_{\textbf{h} \rightarrow \textbf{0}} \frac{f(\textbf{0} + \textbf{h}) - f(\textbf{0}) - Df(\textbf{a})(\textbf{h})}{||\textbf{h}||} = \textbf{0} . directly?
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    Prove that the functin is differentiable at (0, ,0).

    Hi Euler, Thank you for your reply. There's a theorem in my textbook that says that if the first-order partial derivatives of a vector-valued function f exists at a, and if these first-order partial derivatives are continuous at a, then f is differentiable at a. I know how to show the...
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