An Introduction to the t Distribution (Includes some mathematical details)

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 • Introduction to the t ... .

[@ListonFrazier]

Got a statistics exam tomorrow and came across your movies.. Even though I'm quite confident in my knowledge for tomorrow your videos helped me a lot (especially the one on Central Limit Theorem) Thank you!

[@jbstatistics]

I'm glad to be of help!

[@bajdoub]

Thank you so much for this treasure of knowledge that is your channel. Please consider adding this video to the playlist on continuous distributions so it is easy to retrieve :-)

[@mafisha26]

I don't see the point of seating in a classroom, it is a time consuming, this way easy to understand. Thank you JB.

[@jbstatistics]

You're very welcome!

[@cesarmc4533]

there are ways to do that through the internet too ;)

[@no-un3cb]

16? My dude I am a junior in college learning this stuff for the first time

[@3ajamy]

i think you are most professional instructor i have been meet, Big Like From Egypt :)

[@jbstatistics]

Thanks for the very kind words!

[@CULTURE001]

I love coming back to these videos after a lecture. They help fill in all the gaps in terms of explanation. Spot on. They are a massive help. Thank you so much. Please keep em coming. :)

[@sakethvasanthavada4345]

You're creating some serious interest in my course!!!
Thank you!!

[@jbstatistics]

I'm glad to be of help!

[@ffchen5435]

Very intuitive, way better than my professor

[@TimothyChenAllen]

You give great explanations! This was very clear; I really understand the relationship between T and the Standard Normal now. Thanks!

[@jbstatistics]

You are very welcome Timothy. And thanks for the compliment!

[@rushaleegupta7337]

You are the best channel on TH-cam ever

[@moxiaohai81]

you are my best teacher!

[@bonaviafx9434]

Why go to university when i can learn from my house hahah thanks

[@jbstatistics]

You're very welcome!

[@jeffreyanderson5333]

These will be the "basic" stuff in the future. The job market will expect you to integrate knowledge from various disciplines and make use of them in sophisticated ways.

[@swatisahasrabuddhe8759]

hello, just a confusion, the Z formula i have studied is ((Xbar- mu)/ sigma) but in this video, root of n is also included. it will be really very helpful if you could answer this query to me.
by the way the lecture was really great. Thanks in advance

[@jbstatistics]

For a single observation: Z = (X - mu)/sigma. For the mean of n observations: Z = (X bar - mu)/(sigma/sqrt(n)). It's not really two separate formulas, as the former is just the latter with n = 1.

[@puneetkumarsingh1484]

Where can I find the proof which is mentioned at 2:03 in the video?

[@gauravgregrath6606]

really nice.. u r n excellent teacher.. very informative

[@jbstatistics]

+gaurav gregrath Thanks for the compliment!

[@abmxnq]

dude long live and prosper

[@3ajamy]

Your way forces any one to subscribe, it's rely amazing

[@jbstatistics]

Thanks!

[@alexanderconde1477]

Simple but brilliant explanation...thanks :)

[@jbstatistics]

You are very welcome!

[@skg2109]

So what are the cases when we have to divide Z (normal R.V.) by U (Chi² R.V.)?

[@jbstatistics]

This arises in a number of situations. I (briefly) discuss one common one at about the 1:30 mark. In applied situations, we often use the results without explicitly stating the mathematical underpinnings.

[@danielhrichishen2276]

What program are you using to create these videos?

[@jbstatistics]

The base is a Latex/Beamer presentation. I annotate the pdf with Skim, and use Screenflow to record and edit.

[@lettingitrip5854]

Your vids are super cool! Thank you!

[@jbstatistics]

You are very welcome!

[@nightmareghost]

Thanks for the great lesson!

[@jbstatistics]

You are very welcome! Thanks for the compliment!

[@mr.alrightty2902]

thank you so much, this is really helpful

[@coolgreensnake]

love ur videos , keep them coming

[@jbstatistics]

Thanks! There are definitely more to come. I'm hoping for a productive holiday season.

[@mahmoudsheikhelard886]

I love you man :P

[@ArupRoy_fromPlanetEarth]

Thank you, Sir

[@parthi2929]

He is not explaining how the formula are derived instead always only shows the formula upfront and how to handle them. :(

[@jbstatistics]

Deriving the t distribution is far beyond the scope of this video. While not outrageously difficult to do, it's far from trivial, and requires some background knowledge in mathematical statistics (transformations, integration, etc.). In anything but a mathematical statistics course, introducing the t distribution with the derivation would be ridiculous. I may very well derive the t distribution in a future video, but I'll let it be known I'm doing that in the title.

[@gauravnikam969]

u r legend.....

[@jananymadhu9853]

Derive f(t) idhukku and pls

[@AlericResident]

If only I knew/understood what "degrees of freedom" mean :/

[@georgistoilov7954]

2:00 I guess it should be wiDth, not with. There is a typo. The tutorial is great tho!

[@asksaurav]

cool

[@lizzie2trappy54]

Bomboclaat

[@lamalamalex]

Finally got to see the pdf of a t-distribution and boy… it sure is ugly 😂