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Category Archives: Probability
Benfordâ€™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
Posted in Probability, Statistical Inference, Statistics
Tagged Alternative Hypothesis, Benford's Law, Chisquare goodness of fit, Chisquare statistic, Chisquare test, Introduction to statistics, Introductory statistics, Null Hypothesis, pvalue, Statistical Inference, Tests of Significance
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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
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
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
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
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
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 teenmusic idols, to producing a hit television … Continue reading
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
Another look at Titanic passenger data using twoway 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