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Nikolay [14]
3 years ago
10

The first digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9 because we do not write numbers such as 15 as 015. While it i

s reasonable to think that for most real-life data each digit occurs with equal frequency so that each digit 1, 2, ..., 9 has probability 1/9 of being the first digit, this is not true. It is a surprising phenomenon that in many naturally occurring numbers and web-based data the first digit has a probability distribution known as Benford's law.
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.
Specifically, for d = 1, 2, 3, 4, 5, 6, 7, 8, 9, Benford's law states P(first digit is d) = log_10(1+(1/d)) . The distribution of the first digit according to Benford's law, calculated to 3 decimal places, is shown in the table below.
Benford's law
First Digit X 1 2 3 4 5 6 7 8 9
Probability .301 .176 .125 .097 .079 .067 .058 .051 .046
Benford's Law and the Equally Likely Model benford equally likely
The law is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. A surprising variety of data from the natural sciences, social affairs, and business obeys Benford's law.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature).
Numbers that are assigned, such as social security numbers and zip codes, or data with a fixed maximum, such as deductible contributions to individual retirement accounts, or randomly generated numbers, do not follow Benford's law.
The figure below shows how the distribution of the first digit of various naturally occurring and web-based data compares with Benford's law.
benford natural data web data
Figure information. Earthquakes: depth in km of 248,915 quakes, 1989-2009; source National Earthquake Information Center, United States Geological Survey. Minnesota lakes: size in acres of approx. 1100 lakes; source Wikipedia. Births: number of births in each county of the United States (approximately 3200), 2010; source: US Census Bureau. Diggs: total number of diggs for each of the top 1000 diggers at digg.com; source: socialblade.com.
Question 1:
(1a). What is the expected value of the first digit when the first digit follows Benford's law?
expected value (Use 3 decimal places).
(1b). What is the expected value of the first digit when the possible first digits are equally likely?
expected value (Use 3 decimal places).
(1c). What is the standard deviation of the first digit when the first digit follows Benford's Law?
Mathematics
1 answer:
Pie3 years ago
4 0

Answer:

143 i think

Step-by-step explanation:

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1 year ago
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AnnZ [28]
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4 0
3 years ago
a garage floor measures 150 feet by 120 feet. a scale drawing of the floor on grid paper uses a scale of one unit : 15 feet. wha
Nadya [2.5K]
1 unit = 15 feet

150 feet / 1 unit  = 150 / 15 = 10 units

120 feet / 1 unit = 120 / 15 = 8 units

The dimensions of the drawing equates :

10 units by 8 units .

hope this helps!

4 0
3 years ago
A battery manufacturer randomly tests 500 batteries and finds that 3 are defective.
ale4655 [162]
To find this answer, we must first find the percentage of batteries that are defective. We can do this by dividing 3 by 500.

3 / 500 = 0.006

So our percentage of defective batteries is 0.6%.

Now, to find out how many defective batteries would be in a batch of 12000, we just need to multiply the constant (percentage of defective batteries) by the amount in the new batch.

12000 * 0.006 = 72

In a shipment of 12,000 batteries, 72 will be defective, so the correct answer choice would be B.
Hope that helped =)
5 0
3 years ago
Suppose Aldo borrows $5500 at an interest rate of 9% compounded each year assume that no payments are made on the loan how much
ollegr [7]
11,990

9% of 5500 is 495
(495+5500) [one year] x 2 [two years] = $11,990

At the end of 2 years, Aldo will owe $11,990.
3 0
3 years ago
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