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
This
preview
has intentionally blurred sections.
Sign up to view the full version.
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.

This is the end of the preview.
Sign up
to
access the rest of the document.
- Spring '09
- Wostner
- Math, Probability, Benford, Benford distribution
-
Click to edit the document details