Probability Prog. Assignment #1 Biased or Unbiased ?

1. Probability Prog. Assignment #1Biased or Unbiased ? • Is the Dealer worth a trust ? Tzu-Jui Wang Visual Communications Laboratory Department of Communications Engineering, National Central University No. 300, Jhongda Rd., Jhongli City, Taoyuan County 32001, Taiwan (R.O.C.) E-mail:julius0728@gmail.com

2. Begin with Some Words • Programming assignments are usually simpler than writing assignments. • Finish by yourselves within an hour. • Of course, you would possibly copy someone’s work, but that would still cost you an hour.

3. Biased or Unbiased Dice ? • A dealer, who is worth a trust, will always toss the dice fairly. 1st toss 2nd toss 3rd toss

4. Evaluate “Bias” • Get E[Sdice] = 3.5 in expectation. • In your program, E[S1] 1st exp. : Toss 10 times → {2 3 1 4 6 2 2 5 5 3} 2nd exp. : Toss 110 times → {1 2 6 3 2 4 5 2 3 … } 3rd exp. : Toss 210 times → {2 3 4 5 6 1 1 1 2 3 4 5 6 6 6…} . . . . . . 100th exp. : Toss 10000 times → {1 4 6 2 3 4 5 2 3 1 6 2 1 2 6 …} E[S2] E[S3] E[S100]

5. Evaluate “Bias”

6. You Should… • Plot Biask, where k = 1, 2, 3, …, 100. (30%) • Plot E[Sk], where, k = 1,2, 3, …, 100. (30%) • State your findings. • IN YOUR OWN WORDS. (40%) • Submit the report + codeto juliuswang0728@gmail.com, packed into a zip/rar file with the file name “學號_系級_姓名”(e.g. 945003039_通訊五_王任汪.rar)

7. You can… • Use whatever programming language you like. • C, C++, MATLAB, JAVA, …etc. • Due date : 2010.03.26 (Fri.) 14:50 pm • No DELAY is allowed.