# Search results

1. ### Distribution of balls in a box (with a twist)

So would it be a "mixed distribution"?
2. ### Distribution of balls in a box (with a twist)

I'm interested in the distribution of the sizes.
3. ### Combining Distributions (ex. Mixture distribution, copula)

Hi Stephen, Yes, I think a mixture distribution is a very natural way of describing the distribution of the "box". Also, copulas allow a way to describe the joint distribution of the two r.v.'s. Do you know if there any other statistic which combines or links the r.v.'s?
4. ### Distribution of balls in a box (with a twist)

Suppose I have an box (set) containing two different colored balls, red and blue, say. Now, suppose the balls differ in size, where the size of the red balls has one particular distribution and those of the blue another. How can we describe the distribution of the balls in the box?
5. ### Combining Distributions (ex. Mixture distribution, copula)

Hi Stephen, Thank you for your post. I'm sorry if I'm failing to describe the situation clearly. Here's a second attempt... Suppose I take all incidences of loss due to fraud (r.v. X) and those of external circumstances (r.v. Y) and put them in one "box". Then the members of my box can...
6. ### Combining Distributions (ex. Mixture distribution, copula)

The physical units of my variables is $dollars. One random variable represents$'s lost due fraud. The second \$'s lost due to external circumstances. These r.v.'s may come from different distributions but they may not necessarily be independent.
7. ### Combining Distributions (ex. Mixture distribution, copula)

This is a vague question and I apologize in advance for not being able to explain it better. I'm combining r.v.'s from different populations (distributions). The resulting population can be thought to come from a mixture distribution. I think another way of describing the resulting...
8. ### Solve (-1)^x=1

Olivermsun, I believe in complex terms we have log(-1)=i\pi. But again we face the same dilemma as i\pi\ne 0
9. ### Solve (-1)^x=1

You're missing the point. It's not a matter of solving the equation, its the fact that by performing a completely legitimate operation we now have an equation where the RHS does not equal the LHS.
10. ### Solve (-1)^x=1

Ok. So the answer to finding the solution of (-1)^x=1 is clear. But say we didnt know it and wanted to solve it. One approach is to take the log of both sides x\cdot log(-1)=log(1)=0 But now the right hand side is defined where as the left is not! What am I missing?
11. ### Dielectric Boundary Condition Question

MisterX you are amazing! I am grateful. Thank you.
12. ### Dielectric Boundary Condition Question

Hi, I have a question regarding the boundary condition present for a dielectric immersed in a static field. I hope one of you physics guru's can shed some light on this. Suppose we have a dielectric in space subjected to some external static electric field. I have read (without explanation)...
13. ### Dielectric Sphere in Uniform Field

Thank you Jano!
14. ### Dielectric Sphere in Uniform Field

Hi, One of the boundary conditions when solving for the potential, \Phi, outside a dielectric sphere placed within a uniform electric field is \lim_{r→0}\Phi(r,θ)<\infty Can anyone explain/prove why this so. Thanks,
15. ### Conditional Probability - Markov chain

Brilliant!! Thank you.
16. ### Conditional Probability - Markov chain

Hi, I was reading about Markov chains and came across the following statement: "The conditional distribution p(x_n|x_{n-1}) will be specified by a set of K-1 parameters for each of the K states of x_{n-1} giving a total of K(K-1) parameters." In the above we have assumed that the...
17. ### Acadamia vs. Industry - supervisors role

Acadamia vs. Industry -- supervisors role Is there an incentive for supervisors to guide their Ph.D. students to follow an academic career rather than move to industry?
18. ### When y= a constant, how do you find the interval of definition?

If your solution is y=c then dy/dt must have been 0. Unless it was specified that dy/dt=0 on some particular interval, then your solution should be valid for all t.
19. ### 2nd order Linear DE

Hi, When solving a 2nd order Linear DE with constant coefficients (ay''+by'+cy=0) we are told to look for solutions of the form y=e^{rt} and then the solution (if we have 2 distinct roots of the characteristic) is given by y(t)=c_1 e^{r_1 t}+c_2 e^{r_2 t} This is clearly a solution, but...
20. ### Dielectric Sphere in Time Varying Field

Changing E-field and Dielectrics Hi, If I have a spatially uniform field whose magnitude is changing in time (say \vec{E}=E_o\sin(\omega t)\vec{k}) and I place a dielectric in this field, will the perturbation of the field have the same frequency? That is, will the resultant field have a...
21. ### Dielectric Sphere in Time Varying Field

Thanks Marcusl. Unfortunately I didn't find what I was looking for. any other ideas?
22. ### Dielectric Sphere in Time Varying Field

Hi, I'm interested in how a dielectric sphere effects a (spatially) uniform time varying field. I'm sure I'm not the first to inquire about this very topic. Could anyone direct me to a resource? Thanks,
23. ### Dielectric Vs. Resistor

Thank you both. :)
24. ### Dielectric Vs. Resistor

Hi, Do material posses both dielectric as well as resistance properties? I imagine that when there is a difference in potential across a volume of some material, some current will flow (I=V/R <-- the material's resistance), but also the material may become polarized to a certain degree...
25. ### G(E[X],E[Y]) or E[g(X,Y)]

Clearly the second quantity \left\{g(E[X],E[Y])-g(x,y)\right\}^2=0, as E[X]=E[x+noise]=x \qquad \mbox{and}\qquad E[Y]=E[y+noise]=y Since, the first quantity, \left\{E[g(X,Y)]-g(x,y)\right\}^2\ge0 then I guess to answer my question, the first one must be "Better".
26. ### G(E[X],E[Y]) or E[g(X,Y)]

Stephen. Thank you for taking the time. I'm hoping that the meaning of "best" becomes apparent from my second post. I guess I would define it as follows: Which quantity is smaller \left\{E[g(X,Y)]-g(x,y)\right\}^2 or \left\{g(E[X],E[Y])-g(x,y)\right\}^2 where...
27. ### G(E[X],E[Y]) or E[g(X,Y)]

Hi Chiro, Thank you for your reply. The situation is that my z is in fact fixed. Its value depends on two other variables x and y. I have a model/function which calculates the true value of z. That is z=g(x,y) Now, the problem is that I have added noise to my x & y variables: X=x+noise...
28. ### G(E[X],E[Y]) or E[g(X,Y)]

Suppose X and Y are r.v. Suppose also that we get N samples of a r.v. Z which depends on X and Y. That is Z=g(X,Y). Which is a better estimate of the true value of Z? Z=E[g(X,Y)] or Z=g(E[X],E[Y])
29. ### Uniform Field & Poisson equation Mismatch?

Ahh I see. So \rho=0 is an implicit condition for us to have the uniform field in the first place?
30. ### Uniform Field & Poisson equation Mismatch?

Hi, I'm getting some confusing results and cant figure out what is wrong Suppose we have a uniform field E=[0,0,E_z] in a dielectric media. By E=-\nabla\psi we can deduce that \psi(x,y,z)=-z E_z But, taking the Laplacian \nabla^2\psi=\frac{\partial^2 (-zE_z)}{\partial z^2}=0 does...