Uploaded December 2012 | Updated September 2026, 2 hours ago
An introduction to continuous random variables and continuous probability distributions. I briefly discuss the probability density function (pdf), the properties that all pdfs share, and the notion that for continuous random variables probabilities are areas under the curve.
An introduction to continuous random variables and continuous probability distributions. I briefly discuss the probability density function (pdf), the properties that all pdfs share, and the notion that for continuous random variables probabilities are areas under the curve.





![Introduction to the Central Limit Theorem
I discuss the central limit theorem, a very important concept in the world of statistics. I illustrate the concept by sampling from two different distributions, and for both distributions plot the sampling distribution of the sample mean for various sample sizes. I also discuss why the central limit theorem is important in statistics, and work through a probability calculation. (For the most part this is a non-technical treatment, and simply illustrates the important implications of the central limit theorem.)
For those using R, here is the R code to find the probability for the example in this video:
Finding the (approximate) probability that the mean salary of 100 randomly selected employees exceeds $66,000:
1-pnorm(66000,62000,32000/sqrt(100))
[1] 0.1056498
Or, standardizing:
1-pnorm((66000-62000)/(32000/sqrt(100)))
[1] 0.1056498
1-pnorm(1.25)
[1] 0.1056498 Introduction to the Central Limit Theorem](https://i.ytimg.com/vi/Pujol1yC1_A/mqdefault.jpg)




