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Counting without Counting ???

Let me tell you a little dirty secret about the mutual dislike between mathematicians and physicists. It can escalate into a full blown war if diplomacy is not attempted properly.

It happens that a graduate student in theoretical/mathematical physics is looking for five members for his dissertation committee. He has been working closely with three professors in the mathematics department, and 5 professors in the physics department on his dissertation research.

Now comes the monkey wrench.

The mathematics department demands that the chair of the dissertation committee must be a mathematician in order to keep the physicists in check. What? How arrogant! But, there is no other choice if a dissertation committee has to be assembled in time.

Please figure out how may ways this graduate student can choose among his beloved professors, if the chair of the committee must be a mathematician, and the rest of the committee can be a mix of mathematicians and physicists. Post your collaborative group response by Sunday September 26th at midnight Eastern Time.

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There are 3 mathematicians and 5 physicists to choose from

Let us first choose the Chair

Since the Chair has to be a mathematician, there are 3 ...

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Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]
having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).
Demonstrate that the mle theta;hat is a sufficient statistic for theta;.
Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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