# Recent content by Apteronotus

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.