Level 3 Probabilities - Answers

1. Missing values are filled in red.

0.0156	0.0188	0.0188	0.0225	0.0188	0.0225	0.0225	0.027
0.0125	0.0156	0.015	0.0188	0.015	0.0188	0.018	0.0225
0.0125	0.015	0.0156	0.0188	0.015	0.018	0.0188	0.0225
0.01	0.0125	0.0125	0.0156	0.012	0.015	0.015	0.0188
0.0125	0.015	0.015	0.018	0.0156	0.0188	0.0188	0.0225
0.01	0.0125	0.012	0.015	0.0125	0.0156	0.015	0.0188
0.01	0.012	0.0125	0.015	0.0125	0.015	0.0156	0.0188
0.008	0.01	0.01	0.0125	0.01	0.0125	0.0125	0.0156

2. The largest probability value is 0.027 = 0.33 = p43 and occurrs at address 444.

The smallest probability value is 0.008 = 0.23 = p13 and occurrs at address 111.

3. Each probability is a product pi*pj*pk with the factors taken from p1=0.2, p2=0.25, p3=0.25, and p4=0.3. The more factors of p4, the higher the probability; the more factors of p1, the lower the probability. For each N = 1, 2, , ..., in every address length N square, the upper right corner has the highest probability, the lower left has the lowest, and all subsquares on the diagonal have the same probability.

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