Recent content by estro

  1. estro

    How Does the Symmetry of Sine Influence the Distribution of Y = sin(X)?

    Suppose X ~ U[ 0, pi ] What is the distribution of Y=sinX. I have a solution in my notes however I don,t understand the following the second transition: F_Y(y) = P(Y \leq y) = P(X \leq \arcsin(y)) + P(X \geq \pi - \arcsin(y)) = ... Where the P(X \geq \pi - \arcsin(y)) comes from?
  2. estro

    Can a graph with no self loops and odd common neighbors have an Eulerian path?

    Hi Haruspex, I already solved this problem, thanks!
  3. estro

    Can a graph with no self loops and odd common neighbors have an Eulerian path?

    The number of common neighbor vertices is odd, however don't forget about not common vertices.
  4. estro

    Can a graph with no self loops and odd common neighbors have an Eulerian path?

    I'm trying to prove that a graph with the below properties has an eulerian path. 1. Graph has no self loops or parallel edges. 2. Every two different vertices u and v have an odd number of common neighbor vertices. I'm thinking about this problem for a whole day and can't manage to prove...
  5. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    I think I'm closer to the solution as I understand now that: e^{2pi \frac {mk}{n} i} = e^{2pi \frac {mk(mod(n))}{n} i}
  6. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    e^(2pi*(m/n)k) represent same angle when m and n have common divisor, but when they do the whole expressions becomes equal to 1.But I'm still not sure how to translate this into proving what I need to prove. I'm not even sure why the above is true...
  7. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    So I should show that e^{km\frac {2\pi i} {n}} = e^{k\frac {2\pi i} {n}} because m mod(n) != 0?
  8. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    The question is formulated like this: Show that set of values represented by (z^(1/n))^m are the same set of values represented by (z^m)^(1/n). And both these equivalent to set: https://dl.dropboxusercontent.com/u/27412797/q1.png
  9. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    So how can I prove that both expression represent the following: https://dl.dropboxusercontent.com/u/27412797/q1.png
  10. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    Sorry, but I'm not sure I understand. m and n are constants while k goes from 0 to n-1. I do need +2kpi, as I need to prove that both represent the same set of values.
  11. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    This is what puzzlies me: (z^{\frac {1} {n}})^{m} = r^{\frac {m}{n}}e^{\frac {m\theta + 2m \pi k} {n}i} = r^{\frac {m}{n}}e^{\frac {m\theta} {n}i}e^{\frac {2m \pi k} {n}i} (z^m)^{\frac {1} {n}} = r^{\frac {m}{n}}e^{\frac {m\theta + 2 \pi k} {n}i} = r^{\frac {m}{n}}e^{\frac {m\theta}...
  12. estro

    Proving that (z^m)^(1/n)=(z^(1/n))^m

    Homework Statement I want to prove something that seems trivial at first: (z^m)^{1/n}=(z^{1/n})^m , where m and n don't have a common divisor. The Attempt at a Solution When I'm using z=re^{i\theta}, I arrive that above is true if and only if the following is true: e^{ \frac{2\pi \theta...
  13. estro

    Solving y'=\frac{(1+y)^2} {x(y+1)-x^2}: An Alternative Approach

    Thank you very much!
  14. estro

    Solving y'=\frac{(1+y)^2} {x(y+1)-x^2}: An Alternative Approach

    I understand this. but how I can understand that any of one of the tho preserve sign in any domain?
  15. estro

    Solving y'=\frac{(1+y)^2} {x(y+1)-x^2}: An Alternative Approach

    Thanks! But, can I assume that y' is positive or negative in some domain? How can I explain this?