Help please!!! Two stats questions from a biologist...

Hey guys, a biology student (me :) ) needs some help from you maths
people.

Question 1:

I'd like to have an expression (as elegant as possible) for P(x=k),
the prob. of having k positive results for a series of n Bernoulli
experiments. But that's a binomial distribution! Hold on a sec... I
need a formula for P(x=k) in the case where each experiment has a
different probability p(i) i=1,...,n . (So in this case nCk , p**k,
(1-p)**(n-k) where p is constant, don't apply). All the expressions i
wrote range from incorrect to awfully inelegant, so perhaps you guys
come up with a nice one. I know it could be hard to write a complex
expression here so Latex code is just fine. Any ideas?

Question 2:

How to compare the compositional dissimilarity between two proteins?
Each composition can be represented by a 20-component vector, where
the components are the respective fractions for the 20 amino acids, so
of course the components add up to 1. I just learned euclidean
distance does a terrible job at this since it can show as "close" two
compositional profiles that are in fact negatively correlated.
Instead, Pearson's distance (1- r) and Spearman's (1-rho) seem to be
ok for the task. But, in your opinion, which one makes more
statistical sense for this purpose? I'd like the correlation measure
to be as sensitive as possible. So... Pearson's or Spearman's to
compare protein compositions??

Thanks in advance, guys. I'm sure you can help me with this.

Felipe.

.

Relevant Pages

  • Re: zoom feedback
    ... http://en.wikipedia.org/wiki/Perspective_distortion_ (photography) ... distance at which the photograph of the subject is viewed." ... The distance to the subject and the composition you want ... IPAB, Informatics, JCMB, King's Buildings, Edinburgh, EH9 3JZ, UK ...
    (rec.photo.digital)
  • Re: zoom feedback
    ... http://en.wikipedia.org/wiki/Perspective_distortion_ (photography) ... distance at which the photograph of the subject is viewed." ... The distance to the subject and the composition you want ... Moving closer ...
    (rec.photo.digital)
  • Re: zoom feedback
    ... distance at which the photograph of the subject is viewed." ... the scene, determine the composition, including moving ... so you think that whether an object obscures another object or ...
    (rec.photo.digital)
  • Re: zoom feedback
    ... If you are looking at the metric and not at the scene, ... http://en.wikipedia.org/wiki/Perspective_distortion_ (photography) ... distance at which the photograph of the subject is viewed." ... The distance to the subject and the composition you want ...
    (rec.photo.digital)
  • Re: zoom feedback
    ... http://en.wikipedia.org/wiki/Perspective_distortion_ (photography) ... distance at which the photograph of the subject is viewed." ... The distance to the subject and the composition you want ... can be produced by a pin hole camera with no lens at all. ...
    (rec.photo.digital)