Dear Santiago;
I'm planning to set up a simulation experiment and try
to answer your question. I have the following rough
idea: generate a nXk matrix where each k is an
independent random bernoulli variable. In order to
have correlated variables, I'll sort each k and force
correlation between them. Once sorted I will consider
each row from my new sorted matrix as an independent
sample and construct a sample distribution (by summing
across each row). I will treat this new vector as my
sum of correlated bernoulli variables, plot the
frequency distribution and estimate mean and standard
error. Once I have the results from the simulation
experiment I will share them with you. Would you
please send me your mailing address, what university
are you from, country, etc so we keep in touch.
By the way, the problem you pose is a typical example
on how discovery-learning can be used in class to
teach about probability density functions. I'll be
interested to write a paper with you using your
problem and the approach that I propose (simulation
experiment) to discuss how students learn best when
they actively construct their own understanding; that
is learners are encouraged to invent their own
solutions and try out ideas and hypothesis. Here is
where I see the role of computer-generated simulation
experiments in learning probability.
Please keep in touch...
Dr. Jaime Curts
University of Texas Pan Am
1201 W. University Avenue
COE, Room 239
Edinburg, Texas 78539-2999
USA.
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