Recent content by estro

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?

Hi Haruspex, I already solved this problem, thanks!

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

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...

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}

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...

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

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

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

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.

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}...

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...

Thank you very much!

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

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