EXERCISE 2 ON HOMEWORK

Suppose there are 100 undergraduate math education majors at BGSU.  
You are interested in the number theta that are interested in going 
to graduate school in mathematics. You plan on learning about theta 
by taking a survey of 20 math ed majors selected at random.

MTB > # my prior probabilities for theta in the
MTB > # sets [0, 5], [6, 10], [11, 20], [21, 100] are
MTB > #       .3       .4       .25       .05
MTB > 
MTB > # to obtain a simulated sample from this prior:
MTB > #  - I first simulate the intervals (1,2,3,4)
MTB > 
MTB > set c1
DATA> 1:4
DATA> set c2
DATA> .3 .4 .25 .05
DATA> rand 1000 c3;
SUBC> discrete c1 c2.
MTB > 
MTB > # next I simulate uniform values of theta in first interval
MTB > # put the results in c11, uniform values in second interval,
MTB > # put the results in c12, and so on.
MTB > 
MTB > rand 1000 c11;
SUBC> integer 0 5.
MTB > rand 1000 c12;
SUBC> integer 6 10.
MTB > rand 1000 c13;
SUBC> integer 11 20.
MTB > rand 1000 c14;
SUBC> integer 21 100.
MTB > 
MTB > # finally, I put everything together using a let statement
MTB > 
MTB > name c4 'prior_s'
MTB > let 'prior_s'=c11*(c3=1)+c12*(c3=2)+c13*(c3=3)+c14*(c3=4)
MTB > 
MTB > # now I have to tell you the data
MTB > # 20 of the 100 students were randomly selected -- 2 expressed
MTB > # interest in math
MTB > 
MTB > # I update my probabilities using the program 'mod_cont'
MTB >

MTB > exec 'mod_cont'

INPUT THE NUMBER OF THE LIKELIHOOD:
(1-Binomial P, 2-Normal M, 3-Poisson L, 4-Hypergeometric S,
 5-Discrete Uniform N, 6-Capture/Recapture N, 7-Exponential M)
DATA> 4

INPUT   
  (population size, sample size, number of successes)              

DATA> 100 20 2
 
Input number of simulated values:
DATA> 1000

Each dot represents 11 points

              .
            ..:
            :::
          :.:::
          :::::
         .:::::..: :
         :::::::::::
         :::::::::::. .. ........ ........ ...   .... .... .
         +---------+---------+---------+---------+---------+-------prior_s 
Each dot represents 19 points




              .
              :
              :
            :::
            :::
            :::
           .::::::..
          .:::::::::.
         +---------+---------+---------+---------+---------+-------POST_S  
         0        20        40        60        80       100