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\centerline{Mathematics 375 -- Probability and Statistics 1}
\centerline{Problem Set 5}
\centerline{{\it due:} October 22, 2003}
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\noindent
I.  The Maple package for our class now contains a 
procedure that can be used to generate any number
of samples from a given hypergeometric distribution.  
{\it Note:  I just added this on Monday, October 13, so you will need to 
download the package again to get a version including this new procedure.} 
After you have loaded the package, if you enter a command of the 
form:
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\centerline{\tt HypergeometricSample(N,n,r,Num);}
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you will generate {\tt Num} values of a
hypergeometric random variable with parameters: $N =$ total population,
$n =$ sample size, $r = $ number of ``type a'' individuals in the 
total population.  A second command:
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\centerline{\tt HypergeometricPDF(N,n,r,y);}
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computes the values of the hypergeometric pdf with $N,n,r$ as
above, and $y = $ number of ``type a's'' in the sample of size $n$.
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\item{A)}  An electronic device contains 15 components, of 
which 4 are defective.  5 components are selected at random
and tested.  Simulate the testing process using the 
{\tt HypergeometricS} procedure three times, with {tt Num} = 10, 
then 100, then 1000.  (Note:  This means 10 random selections of
5 components to test, then 100, then 1000.)
Compute the frequencies of the different numbers of 
defectives observed and illustrate with frequency histograms
using 5 ``bins'' centered at 0,1,2,3,4 to match the usual set-up
for a probability histogram.  What happens as {\tt Num} increases?
\item{B)}    Using the Maple procedures described above,
compute the theoretical probabilities that $0,1,2,3,4$ defective 
components are found among those tested.  How do your results from 
part A compare to the theoretical values in this part?
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\noindent
{\it From the text:} 3.85,86,87,89,95,97,98,99,100,111,114,117,118,121,126.
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