Recent content by obesogen

Yes, you're right--my states are actually continuous. I am trying to to discretize them so I can use learning algorithms that operate on tables. That being the case, the actions I choose to be available for the agent is also a discrete set. My system is in discrete time, also. My idea behind...

Sorry for being vague. I'm looking at the entropy of P(state j | state i,action a), so for a system obeying the Markov property (which this one does), the probability distribution should become sparser and sparser as the state space is better represented, ideally being 1 for one state and 0 for...

Thanks for the reply. The case is approximating an unknown probability distribution with a histogram. I'm actually trying to figure out how many 'bins' i need to discretize the state space in a dynamical system, so I am looking for the number of bins that sufficiently decreases the entropy...

Any ideas at all?

I'm wondering if there's an expression/correction for finding the entropy of a density using histograms of different bin sizes. I know that as the number of bins increases, entropy will also increase (given a sufficient number of data points), but is there an expression relating the two? All I...

Ah, now I understand the use of 1-F(w), etc. A very useful trick, indeed. Thanks a lot, this was very helpful.

I must still be missing something here. Here's what I'm getting for 0<w<1, for example. Thanks for your patience. G(w)=P(XY>w)=\int P(Xy>w|Y=y)f_Y(y)dy \\ =\int_0^1 P(X>w/y)f(y)dy+\int_{-1}^0 P(X<w/y)f(y)dy \\ =\int_0^1...

Ok, that makes sense, but I don't see how it helps my integral problem, since I still have to compute essentially the same integral. Also, I realized that the reason I was having a lot of trouble was that log|x| actually cannot be integrated using those bounds.

Thank you for the reply, although I am not sure I understand your suggestions. I thought the general strategy to these types of problems was to find the cdf and differentiate. In this way, I don't know how P(W>w) can be of particular use. Are you suggesting a different approach? I tried taking...

Homework Statement If X,Y are independent RVs ~ U[-1,1], and W=X*Y, find the density of W.Homework Equations The Attempt at a Solution I feel my approach is right, but the bounds of my final integral don't make sense. F_{XY}(w)=P(XY \leq w)=\int_{-\infty}^{\infty} P(XY \leq w | Y=y)*f_Y(y)dy...