Examining a list of the heights of the 60 tallest buildings in the world by category...
- Examining a list of the heights of the 60 tallest buildings in the world by category shows that 1 is by far the most common leading digit, irrespective of the unit of measurement. It turns out that the Newcomb-Benford Law predicts this phenomenon quite well, even for digits 2 through 9. This law states that the probabilities for the digits 1 through 9 to be the first digit in these building heights are approximately:
|
Digit |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Prob. |
0.30 |
0.18 |
0.12 |
0.10 |
0.08 |
0.07 |
0.06 |
0.05 |
0.04 |
a. If you were to randomly pick one of the digits between 1 and 9 using a random number generator (so not using the Benford Law above), what is the probability for each digit? [4 points]
b. What is the probability of 4 or 6 as the first digit by (i) the Newcomb-Benford Law as given by the table above and (ii) random selecting these? [6 points]
Homework Answers
a)
probability for each digit =1/9 = 0.1111 (since each of 9 digit are equally likely)
b(
probability of 4 or 6 as the first digit by Newcomb-Benford Law
=0.1+0.07 =0.17
(ii) random selecting these =2/9 =0.2222
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Examining a list of the heights of the 60 tallest buildings in
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