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RESAMPLING SOLUTIONS TO PTOBLEMS

Ghermay Araya asmarina at next03epsl.wam.umd.edu
Thu Sep 30 16:33:54 EST 1993

```SOLUTIONS AND PROBLEMS TO PREVIOUS POSTING:

Resampling, (bootstrapping, etc.), is revolutionizing the practice of
statistic, and the way it is taught.  For articles, and information on
software + books, results of classroom trails, and descriptions of pending
projects in which teachers can become involved, contact the University of
Maryland's Resampling Project. We are especially interested in class
testers.  Contact:
Resampling Project,
attn. P.G. Bruce
University of Maryland,
College Park, MD  20742.
Phone: 703-522-2713
FAX 703-522-5846
email pcbruce at wam.umd.edu

(mark attn. P. C. Bruce).
please provide  both  postal and email address.

SOLUTIONS:

Solution, Puzzle 1:

1.  Three urns - "0,0"; "0,1"; "1,1".

2.  Choose an urn at random. [Can do this on the computer

with random selection of urn numbers, and then "If"]

3.  Choose the first element in the chosen urn's vector.  If

"1", stop trial and make no further record.  If "0", continue.

4.  Record the second element in the chosen urn's vector on

the scoreboard.

5.  Repeat (2 - 5), and calculate the proportion "0s" on

scoreboard. (Answer should be 2/3.)

NUMBERS (1 2 3) a         '"1" denotes a selection of urn 1 (u1),
'"2" urn 2, "3" urn 3
NUMBERS (6 6) u1          '"u1" has two pennies (6's)
NUMBERS (7 7) u2          '"u2" has two nickels (7's)
NUMBERS (6 7) u3          '"u3" has one penny & one nickel
REPEAT 1000
SAMPLE 1 a b            'Select an urn at random
IF b =1                 'If urn selector says urn 1
SHUFFLE u1 u1         'shuffle urn 1
TAKE u1 1 c11         'take one coin from urn 1, call it c11
IF c11=6              'if the coin is a penny
TAKE u1 2 c12       'take the second coin
IF c12=6            'if the second coin is a penny
SCORE 6 z         'keep track of the second coin result
END                 'end IF conditions
END
END

IF b =2                 'if urn selector says urn 2
SHUFFLE u2 u2         'etc. as above
TAKE u2 1 c21
IF c21=6
TAKE u2 2 c22
IF c22=6
SCORE 6 z
END
END
END

IF b =3
SHUFFLE u3 u3
TAKE u3 1 c31
IF c31=6
TAKE u3 2 c32
IF c32=6
SCORE 6 z
END
END
END

END                        'End the experiment, go back and
'repeat until 1000 repetitions
'are complete
COUNT z = 6 k
DIVIDE k 1000 kk
PRINT kk

Answer:        KK       =       0.34

Solution:  Puzzle 2

1.  Put a white ball (later have the computer call it "7" to

avoid confusion) or black (call it "8") in the urn with

probability .5.

2.  Put in a white and shuffle the two balls.

3.  Take out a ball.  If black, stop and make no record.

4.  (If result of (3) is white):  Take out the remaining

ball, examine, and reco
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