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 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
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