math80.sample quiz11 - latest edit Tuesday:12 pm wostner...

latest edit: Tuesday, March 24, 01:12 pm
wostner : probability : benford distribution exercises
©2006-2009 ulf wostner<[email protected]> benford distribution
Definition: A random variable X with
DOMAIN = {1, 2, 3, 4, 5 ,6 ,7 , 8, 9}
and probability function
p(d) = log( (d+1) ⁄ d)
is said to have Benford Distribution , and we will write
X = BENFORD
exercises
1. Using your calculator, calculate all the probabilities p(d) and enter them into the p(d) column
below.
d p(d)
d ⋅ p(d) d
2
⋅ p(d)
1 0.3010
2
3
4
5
6
7
8
9
1.0000
2.
Answer: For example, p(9) = 0.0458. Verify that Σp(d)=1
3.
Calculate both E(X) and SD(X) . Use our usual shortcut formulas for E(X) and SD(X), and show
your calculations in the table above. Answer: E(X) = 3.4402, SD(X) = 2.4610

4.
Create a table showing the cumulative frequencies for p(d), completing the table below.
d p(d) cum(d) 1-cum(d)
1 0.3010
2
3 0.6021
4
5
6
7
8
9 1.0000
1.0000
5.
Use your table above to calculate P(X ≥ 5). Answer: …
6.
Use your table above to calculate P(X < 5). Answer: …
7.