Statistics 101: Uniform Probability Distributions 

Man, I wish I had more teachers like you in my educational career! You are the real deal, sir.

You're great. I'm studying at one of the top universities worldwide and I got nothing close to this out of the lecturers. That's what happens, they are too snobby to teach properly.

your opener really just made me cry, so thank u so much for putting it in. I really needed that :')

Hello and thank you for the question! The easy truth is that the "12" is built in to the uniform distribution variance formula. It is a given. I'm sure I could reverse engineer the derivation somehow but for now I will enjoy the rare occasion in statistics when something us just given to us. :) All the best, B.

Thank you Brandon for such detailed explanations and taking time to explain every concept precisely. Please keep posting your videos. You are of lot of help.

Thank you sooooo much! I am taking online statistics and I am in week 4. This is the first week I had trouble understanding, and my book was no help. You are awesome! Please keep providing this service. My College Math professor was like you and that's how I got an A. She broke everything down and was an amazing professor. You're an amazing teacher also, so thank you again.

Superb, now I understand between uniform or discrete and continuous probabilities. You are great. Thank you Brandon.

Thank you for your patience in teaching! Never understood this concept more clearly before. Finally understood now crystal clear.

The level of details is amazing

Great Job, May Allah bless you and grant you success in this life and the hereafter !

Its a good day when I can finally understand statistics!! I am so glad to have found your channel Brandon! Watching all your playlists and hoping to bring my grade back up.

Thank you for do this video and the others. You've managed to do in 30 minutes what my professor hasn't been able to achieve in weeks. Again, many, many thanks.

My teacher spent half a term talking about this and I didn't get a thing from that class. I love your video so much and you've definitely saved my life!

great.... i wish i saw this since the beginning of the statistics course!!! THANK YOU

Your videos are extremely helpful. The pace in which you teach the subject matter is perfect. Thank you so much! You will be a reference I will continue to use.

Brandon,thanks for doing this video. I was grinding out the calculations without any clarity and no enjoyment, but after watching your video on the uniform probability destination, I came away with,at least an inkling, for what a powerful conceptual tool, it could be. Now instead of arbitrary, the normalcdf function on my calculator actually seems pretty cool !

For me, it is the best tutorial for statistics specially to those who are taking statistics for the first time, and for those students who have the understanding using geometric figure.

Thank you, Brandon! Applause!!! I hope to find more of your videos during my studies!

This was the best explanation as to why the probability of any one specific value in a continuous distribution is zero I have ever heard.

Thank you for this video, but more so for the encouragement. I am 4 classes away from completing my Masters and I get this curve ball for an applied stats class. Frustrated and discouraged is an understatement. I feel a bit relieved after these series of videos. I hope to continue to be able to apply your knowledge to the success of my course. Thanks again

This video was fantastic!! And you set yourself apart by adding the motivation :) Thank you.

you Sir just helped me get an A, I can't thank you enough

Excellent presentation there, Mr. Foltz! Very thorough with easy to follow visuals. Thanks for putting this up on RU-vid.

Thank you so much, Brandon! You literally saved my life! As I am studying for the CFA, watched other videos and tried to read the book and still made ZERO sense to me. After watching this lesson it clicked! Your motivational words to stay positive and keep our heads up sure helped me not to give up!

OMG I LOVE This guy!!! you just explained something that took me for ever to google. THANK YOU

Hey just wanted to say good job and thank you for making this video. It was a lot of help and I really liked how you went through multiple questions to help clarify the material.

Another great video, love it! Everything is crystal clear!

Great Video!!!! Helped me understand so much better and I love how positive you are! I'll keep watching!

That was absolutely amazing. Didn't understand it at all with my instructor but now I get it!!! I subscribed and will be definitely be watching more. Thanks so much.

thank you for your encouragement!!!! you're awesome!!!

Really got it...i fed up with my lecturer.....thank u so much sir.....

This video just helped me figure this section out. I've been stumped for the last week.

Learning about Continuous Distribution has never been such easy. Thank you so much. 😀

Thank you so much for all of your help. Your videos have helped me tremendously.

I watched couple videos. I liked them. I will watch all you statistics videos.

Thank you for your videos, they are a great help.

Thank you so much for the videos, they are all very helpful.

Very helpful and clear explanation. Thank you for making this!

Wow terrific lesson, articulated very well! This helped clear up many things :)

Hi Brandon...This is me again. I have become a fan of yours Brandon...You are absolutely spot on with your visual explanations..God Bless You for taking effort and time in doing these videos..Thanking you wholeheartedly!!!

Thumbs up for the positive reinforcements in your video. "Believe in yourself... You can do it."

Absolutely Brilliant Professor !!! Thanks so much !!!

This is very helpful! Thank you so much!

hello i am Joseph i am in Grade 9 and 15 years of age, Thank you bro really liked the video i really needed help in understanding this, this would also help me because i want to become and engineer , i also have problems in understanding the chemistry and statistics and keen to watch your other videos :)

Hi Rachel! Thank you so much for your nice comment. I am sure your instructor means well but having been there myself, I know we often get pulled in many directions at once. :) I am just trying to light the path, students like yourself actually have to do the walking. Keep learning! All the best, B.

Thank you Marcus!

The introductions makes me react like "Ooooff! WOW!". I guess, I really need that motivation~! With that, thank you!

Thank you, Brandon, this video is very informative!!!!

Great video, Great motivation... Keep making videos, and keep sharing your passion for teaching =)!

Yet again a great video

You are an awesome teacher!

you have made it easy to understand....thanks

You're are really fantastic .... Neatly explained thank you very much

Great video, I learned - Thanks!!

Thank you kind sir ..Your lessons are great.

Oh thank you so much!

Great explanation, Thank you.

love the way u teach thanks a lot

Great job explaining. Thank you!

honestly your the best my professor makes no sense but this is so easily digestible I understand it so much better now thank you

Thank you! this video is well done.

Thank you so much! This lecture was really helpful :)

Amazing!!! Can you also explain other continuous probabilities and Generating Functions with Continuous Probabilities?

Another excellent job!

Really nice video! Helped me alot, thanks!

Thanks for the help, my professor doesn't teach well and actually puts up links to your videos in out class lectures.

YOU are just awesome, awesome & awesome.

awesome video thank you so much!!

Subbed!!! ur a great help! thanks for the video!!

Thanks v much, excellent video

you are a savior of my life....

awesome sir thank you very much it become very easy to understand the distribution taught by you

Thanks for uploading this video really helpful

All videos are just awesome!! (y)

perfect , please continue making such videos

Great video and pep talk in the beginning, one question I have to ask. We are taking a proportion of the line segment to represent the area of the triangle. So we are saying that ratio of line 1 and line 2 is the same as the ratio of the area of rectangle A and rectangle B. Will be great if you can confirm. Thanks

Amazing thank you so much.

Thank you for the great help:)

Brandon, you are amazing.

very helpful! thank you so much sir! :)

What's the idea of dividing by 12 for the variance of a uniform distribution? I understand the variance for a population is found by dividing by n number of data points (or n-1 for a sample), and since you can't meaningfully divide a continuous uniform distribution by infinite data points, you would take a continuous sum (or the integral) of the difference between a and b. But why 12 for a uniform distribution? Is that just how the integral simplifies down?

just excellent!!!!!!!!

thx for ur awesome video man

you are great..!

Excelent as always...!! :)

Your "don't freak out" comments are actually quite comforting lol

Clear and simple

Very nice work :)

Thank you for this video, the instructions in class where difficult to understand, however you seemed to explain uniform distribution in a way that I can understand. Thank you!!!

THANKS MAN U ARE AWSOME

Excellent thanks

please continue making such videos. I did loose you on some steps. you talked about x2-x1/b-a.

very helpful!

Thank you sir very very much

Thank you!

Thanks a lot :)

made easy to understand ........

you've just earn a new subscription

This is great Brandon. Do you work as a lecturer?

hi! i was just wondering if its the same thing when p(x) is said to be greater or equal to (lets say for your example) 21 and less than or equal to 25? the video was extremely helpful! thank you so much... but i was just left with that tiny question