Category Archives: Probability

Cryptography and Presidential Inaugural Speeches

Given a letter in English, how often does it appear in normal usage of the English language? Some letters appear more often than others. For example, the last letter Z is not common. The vowels are very common because they … Continue reading

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Benford’s Law and US Census Data, Part II

The Benford’s law is a probability model that is a powerful tool for detecting frauds and data irregularity. The first digit (or leading digit) of a number is the leftmost digit and can only be 1, 2, 3, 4, 5, … Continue reading

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Benford’s Law and US Census Data, Part I

The first digit (or leading digit) of a number is the leftmost digit (e.g. the first digit of 567 is 5). The first digit of a number can only be 1, 2, 3, 4, 5, 6, 7, 8, and 9 … Continue reading

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Is It Possible to Spot Fraudulent Numbers?

People engage in financial frauds have a need to produce false data as part of their criminal activities. Is it possible to look at the false data and determine they are not real? A probability model known as the Benford’s … Continue reading

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Rolling Dice to Buy Gas

The price of gas you pay at the pump is influenced by many factors. One such factor is the price of crude oil in the international petroleum market, which can be highly dependent on global macroeconomic conditions. Why don’t we … Continue reading

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The Middle 80% Is Not 80th Percentile

A student sent me an email about a practice problem involving finding the middle 80% of a normal distribution. The student was confusing the middle 80% of a bell curve with the 80th percentile. The student then tried to answer … Continue reading

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Coin Tossing and Family Size

If you a toss a coin 9 times, what is the probability of obtaining 8 heads and 1 tail? I just tossed one penny 9 times and the following is the resulting sequence of heads and tails. The above little … Continue reading

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The Osmond Brothers – a Binomial Example

According to Wikipedia, the Osmonds are an American family music group with a long and varied career – a career that took them from singing barbershop music as children, to achieving success as teen-music idols, to producing a hit television … Continue reading

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The Birthdays of the Presidents of the United States

How likely is it to find two people with the same birthday in a group of partygoers? If the group only has 2 or 3 people, it is probably not likely. So how many people do you need to have … Continue reading

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Another look at Titanic passenger data using two-way tables

It is well known that among the passengers in Titanic, women and children were more likely to survive. It is also well known that first class passengers were even more likely to survive than passengers in the other classes. We … Continue reading

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