Thanks, I had figured that out.

Now I'm having trouble finding the MLE, because i'm having trouble breaking up the sum for the total score function.

I know that each x_i ~ p*(x_i,r) = x_i / ( r sqrt(r^2-x^2)

s(x_i,r) = -1/r - r/(r^2-x_i)^2

I need to find s(x,r) = \sum s(x_i,r)

When I do that, I can't seem to separate it into something solveable. Does anyone have any tips on manipulating the sum to give the score function in terms that will put the sum only on the x_i's

Thanks,

Stephen


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/m29 sorry that should read:

s(x_i,r) = -1/r - r/(r^2-x_i^2)

For problem 4, which variable is uniformly distributed? Is the distance of a cross-section or the radius of a sphere itself? How can we decide this? In both cases, we get similar pdf but not the same.

/m31 answer: Your question is perhaps the part of the problem that is conceptually the least clear. I think the answer is that the point at which each organelle is aliced is uniformly distributed, hence the observed radius of the disk obtained from the organelle is not uniformly distributed.

/m29 answer: Remember, you can maximize f(x) by setting its derivative to zero only when the optimal x is in the interior of the allowed range for x.

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