# Posts Tagged ‘ probability ’

## Mathematical and Applied Statistics Lesson of the Day – The Motivation and Intuition Behind Markov’s Inequality

$Mathematical and Applied Statistics Lesson of the Day – The Motivation and Intuition Behind Markov’s Inequality$

Markov’s inequality may seem like a rather arbitrary pair of mathematical expressions that are coincidentally related to each other by an inequality sign: where . However, there is a practical motivation behind Markov’s inequality, and it can be posed in the form of a simple question: How often is the random variable “far” away from […]

## Mathematical Statistics Lesson of the Day – Markov’s Inequality

$Mathematical Statistics Lesson of the Day – Markov’s Inequality$

Markov’s inequality is an elegant and very useful inequality that relates the probability of an event concerning a non-negative random variable, , with the expected value of .  It states that where . I find Markov’s inequality to be beautiful for 2 reasons: It applies to both continuous and discrete random variables. It applies to any non-negative […]

## Video Tutorial – Calculating Expected Counts in a Contingency Table Using Joint Probabilities

In an earlier video, I showed how to calculate expected counts in a contingency table using marginal proportions and totals.  (Recall that expected counts are needed to conduct hypothesis tests of independence between categorical random variables.)  Today, I want to share a second video of calculating expected counts – this time, using joint probabilities.  This method uses […]

## The odds of a cluster of airplane accidents

August 2, 2014
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Recently, there have been a lot of airplane accidents. July, 17th 2014, Hrabove, Ukraine, Malaysia Airlines, Boeing 777, fatalities 298 (/298) July, 23rd 2014, Magong, Taiwan, TransAsia Airways, ATR 72-500, fatalities 47 (/58) July, 24th 2014, Aguelhok, Mali, Air Algerie, Mc Donnell Douglas MD-83, fatalities 116 (/116) It is simple to find a lot of datasets about airplane crashes. For instance on http://ntsb.gov/aviationquery. The dataset is nice, with a lot…

## Les anniversaires de vos amis sur Facebook

July 21, 2014
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$Les anniversaires de vos amis sur Facebook$

J’ai découvert avec un peu de retard le joli billet Les anniversaires de vos amis sur Facebook, qui tentait de répondre à la question Si je possède  amis, quelle est la probabilité qu’il y ait au moins un jour dans l’année où je n’ai pas d’anniversaire à souhaiter ? Ce problème, on peut aussi l’analyses en posant plutôt la question suivante, Il y a en tout 365 jours dans une année. Combien d’amis…

## Video Tutorial – Allelic Frequencies Remain Constant From Generation to Generation Under the Hardy-Weinberg Equilibrium

The Hardy-Weinberg law is a fundamental principle in statistical genetics.  If its 7 assumptions are fulfilled, then it predicts that the allelic frequency of a genetic trait will remain constant from generation to generation.  In this new video tutorial in my Youtube channel, I explain the math behind the Hardy-Weinberg theorem.  In particular, I clarify […]

## Frequentist inference only seems easy

July 1, 2014
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Two of the most common methods of statistical inference are frequentism and Bayesianism (see Bayesian and Frequentist Approaches: Ask the Right Question for some good discussion). In both cases we are attempting to perform reliable inference of unknown quantities from related observations. And in both cases inference is made possible by introducing and reasoning over […] Related posts: Bayesian and Frequentist Approaches: Ask the Right Question Automatic bias correction doesn’t…

## Mathematical and Applied Statistics Lesson of the Day – Don’t Use the Terms “Independent Variable” and “Dependent Variable” in Regression

$Mathematical and Applied Statistics Lesson of the Day – Don’t Use the Terms “Independent Variable” and “Dependent Variable” in Regression$

In math and science, we learn the equation of a line as , with being called the dependent variable and being called the independent variable.  This terminology holds true for more complicated functions with multiple variables, such as in polynomial regression. I highly discourage the use of “independent” and “dependent” in the context of statistics […]

## On Hoeffding’s identity

June 18, 2014
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In 1940, Wassily Hoeffding published Masstabinvariante Korrelationstheorie, which was an impressive paper. For those (like me) who unfortunately barely speak German, an English translation could be found in The Collected Works of Wassily Hoeffding, pu...

## Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Can Apply to the Sum

$Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Can Apply to the Sum$

The central limit theorem (CLT) is often stated in terms of the sample mean of independent and identically distributed random variables.  An often unnoticed or forgotten aspect of the CLT is its applicability to the sample sum of those variables, too.  Since , the sample size, is just a constant, it can be multiplied to to obtain […]