Uploaded November 2013 | Updated September 2026, 2 hours ago
An introduction to the t distribution, a common 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 mathematical details regarding the t distribution (the pdf, mean, variance, how the distribution arises). Depending on your needs, this may not be important to you. In that event, I also have a video with a less technical introduction to the t distribution, available at youtu.be/Uv6nGIgZMVw.
An introduction to the t distribution, a common 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 mathematical details regarding the t distribution (the pdf, mean, variance, how the distribution arises). Depending on your needs, this may not be important to you. In that event, I also have a video with a less technical introduction to the t distribution, available at youtu.be/Uv6nGIgZMVw.









![Introduction to the t Distribution (non-technical)
A brief non-technical introduction to the t distribution, how it relates to the standard normal distribution, and how it is used in inference for the mean.
For those that use R, below are the R codes to find the values found in the video.
z value for a 95% interval:
qnorm(.975)
[1] 1.959964
t value for a 95% interval (5 DF)
qt(.975,5)
[1] 2.570582
t value for a 95% interval (10 DF)
qt(.975,10)
[1] 2.228139 Introduction to the t Distribution (non-technical)](https://i.ytimg.com/vi/Uv6nGIgZMVw/mqdefault.jpg)
