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.
I work through an example of finding the median, areas under the curve, and the cumulative distribution function for a continuous probability distribution. I assume a basic knowledge of integral calculus. I derive the mean and variance of this distribution in another video: http://youtu.be/Ro7dayHU5DQ.
I work through an example of deriving the mean and variance of a continuous probability distribution. I assume a basic knowledge of integral calculus.
A brief introduction to the (continuous) uniform distribution. I discuss its pdf, median, mean, and variance. I also work through an example of finding a probability and a percentile. I don’t do any integration in this video.
An introduction to the normal distribution, often called the Gaussian distribution. The normal distribution is an extremely important continuous probability distribution that arises very frequently in probability and statistics.
I discuss standardizing normally distributed random variables (turning variables with a normal distribution into something that has a standard normal distribution). I work through an example of a probability calculation, and an example of finding a percentile of the distribution. It is assumed that you can find values from the standard normal distribution, using either … Read more
An introduction to the normal approximation to the binomial distribution. I discuss a guideline for when the normal approximation is reasonable, and the continuity correction. I work through examples of greater than, greater than or equal to, less than, and less than or equal to, and include plots that may help students to visualize the … Read more
An introduction to normal quantile-quantile (QQ) plots (a graphical method for assessing whether a set of observations is approximately normally distributed). I discuss the motivation for the plot, the construction of the plot, then look at several examples. In the examples I look at what a normal quantile-quantile plot looks like when sampling from various … Read more
A brief introduction to the chi-square distribution. I discuss how the chi-square distribution arises, its pdf, mean, variance, and shape.
An introduction to the t distribution, a commonly used continuous probability distribution. I discuss how the t distribution arises, its pdf, its mean and variance, and its relationship to the standard normal distribution. I illustrate the relationship between the t distribution and the standard normal distribution through a series of plots. This video contains some … Read more