Category Archives: statistics

An Expected Value Connection Between Order Statistics from a Discrete and a Continuous Distribution

Years ago, in the course of doing some research on another topic, I ran across the following result relating the expected values of the order statistics from a discrete and a continuous distribution.  I found it rather surprising. Theorem: Fix n, and … Continue reading

Posted in order statistics, probability, statistics | Leave a comment

Operations Research Makes List of Top 5 STEM Professions Employing Women

My February 2016 issue of ORMS Today says that “operations research analyst” is the STEM (Science, Technology, Engineering, and Mathematics) profession with the third-highest percentage of women.  The percentage of OR analysts who are women is 55.4%.  I’m glad to see … Continue reading

Posted in gender, operations research, optimization, statistics | Leave a comment

Independence of the Range and Minimum of a Sample from an Exponential Distribution

A few years ago I answered a question on math.SE about the distribution of the sample range from an exponential (1) distribution.  In my answer I claim that the range and the minimum of the sample are independent, thanks to the … Continue reading

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Picking Random Points on a Circle (Not a Disk)

How do you select points at random on a circle?  By “circle” I mean the outside of a disk, not its interior.  In this post I’m going to discuss two methods: (1) Selecting an angle at random on and taking … Continue reading

Posted in probability, simulation, statistics | 2 Comments

A Math Error in the New Yorker

I normally use this blog to talk about mathematical questions that interest me.  However, I saw a math error in the New Yorker yesterday that I think is worth commenting on. James Surowiecki has an article (The Mobility Myth) arguing that … Continue reading

Posted in journalism, statistics | 2 Comments

Tail Bounds of the Normal Distribution

The question of bounding the tails of the normal distribution has popped up a couple of times on math.SE lately.  This is an easy-to-prove but useful result, and so it’s worth talking about. The standard normal probability density function is … Continue reading

Posted in probability, statistics | 6 Comments