# Posts Tagged ‘ probability ’

## Video Tutorial – Rolling 2 Dice: An Intuitive Explanation of The Central Limit Theorem

$Video Tutorial – Rolling 2 Dice: An Intuitive Explanation of The Central Limit Theorem$

According to the central limit theorem, if random variables, , are independent and identically distributed, is sufficiently large, then the distribution of their sample mean, , is approximately normal, and this approximation is better as increases. One of the most remarkable aspects of the central limit theorem (CLT) is its validity for any parent distribution of […]

## Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Applies to the Sample Mean

$Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Applies to the Sample Mean$

Having taught and tutored introductory statistics numerous times, I often hear students misinterpret the Central Limit Theorem by saying that, as the sample size gets bigger, the distribution of the data approaches a normal distribution.  This is not true.  If your data come from a non-normal distribution, their distribution stays the same regardless of the […]

## Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

$Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function$

In an earlier video, I introduced the definition of the hazard function and broke it down into its mathematical components.  Recall that the definition of the hazard function for events defined on a continuous time scale is . Did you know that the hazard function can be expressed as the probability density function (PDF) divided by the […]

## Useful for referring—2-25-2014

February 25, 2014
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Interview with Nick Chamandy, statistician at Google You and Your Research +  video Trustworthy Online Controlled Experiments: Five Puzzling Outcomes Explained A Survival Guide to Starting and Finishing a PhD Six Rules For Wearing Suits For Beginners Why I Created C++ More advice to scientists on blogging Software engineering practices for graduate students Statistics Matter […]

## Bivariate Densities with N(0,1) Margins

February 19, 2014
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$\mathcal{N}(0,1)$

This Monday, in the ACT8595 course, we came back on elliptical distributions and conditional independence (here is an old post on de Finetti’s theorem, and the extension to Hewitt-Savage’s). I have shown simulations, to illustrate those two concepts of dependent variables, but I wanted to spend some time to visualize densities. More specifically what could be the joint density is we assume that margins are  distributions. The Bivariate Gaussian distribution Here,…

## Video Tutorial: Breaking Down the Definition of the Hazard Function

$Video Tutorial: Breaking Down the Definition of the Hazard Function$

The hazard function is a fundamental quantity in survival analysis.  For an event occurring at some time on a continuous time scale, the hazard function, , for that event is defined as , where is the time, is the time of the occurrence of the event. However, what does this actually mean?  In this Youtube […]

## What’s Warren Buffett’s \$1 Billion Basketball Bet Worth?

January 23, 2014
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A friend of mine just alerted me to a story on NPR describing a prize on offer from Warren Buffett and Quicken Loans. The prize is a billion dollars (1B USD) for correctly predicting all 63 games in the men’s Division I college basketball tournament this March. The facebook page announcing the contest puts the odds at 1:9,223,372,036,854,775,808, […]

## Machine Learning Lesson of the Day – Classification and Regression

$Machine Learning Lesson of the Day – Classification and Regression$

Supervised learning has 2 categories: In classification, the target variable is categorical. In regression, the target variable is continuous. Thus, regression in statistics is different from regression in supervised learning. In statistics, regression is used to model relationships between predictors and targets, and the targets could be continuous or categorical.   a regression model usually includes 2 components to […]

## 37% chance

December 21, 2013
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$n\times n$

I don’t know if you ever realized, before, but it is quite common to have 37% chance that something happened (or actually “not happened” if we want to be more rigorous). For instance, consider a  grid, and draw  points randomly (and uniformely). Then, around 37% cells are empty. Or if you consider a cell, on that grid, there is 37% chance, that the cell is empty. You can look, on the…

## On Wigner’s law (and the semi-circle)

December 17, 2013
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$n\times n$

There is something that I love about mathematics: sometimes, you discover – by chance – a law. It has always been there, it might have been well known by some people (specialized in some given field), but you did not know it. And then, you discover it, and you start wondering how comes you never heard about it before… I experienced that feeling this evening, while working on the syallbus for…