An Introduction to the Continuous Uniform Distribution

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.
(This video contains a (small) typo at 6:22, that I corrected with an annotation. A new version of this video with the mistake corrected can be found at • Introduction to the Co... .)

Пікірлер: 178

  • @Leeannannaeel
    @Leeannannaeel7 жыл бұрын

    I never comment on anything, but this is so excellent. Immediately understood a concept I have been trying to understand for twelve hours.

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    I'm glad to be of help!

  • @mulchdiggums3016

    @mulchdiggums3016

    5 жыл бұрын

    You and me both! This makes SO much sense when explained properly

  • @rahulkatara6650

    @rahulkatara6650

    4 жыл бұрын

    Do you get the logic of formula of Variance?

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    Thanks for the feedback and compliment. For a continuous random variable, the pth percentile is the value of the variable that has p% of the area to the left. In the video I say "the 20th percentile is the value of the variable such that the area to the left is 0.2, or 20%". I'm not sure how much clearer I could make that, without going off on a tangent about the meaning of percentiles. At this point in a stats course students have usually been introduced to the concept of percentiles already.

  • @sheriffpina4102
    @sheriffpina41024 жыл бұрын

    I have a professor that truly doesn’t understand the profession and subject he has selected. His poor choice has me searching through KZread videos for an idea to get started on my exams/homeworks. This video has helped me tremendously, you’ve earned yourself a like and a new subscriber!

  • @CatholicSeoul
    @CatholicSeoul6 жыл бұрын

    Good instructors are usually found on KZread and not in classrooms! Thanks!

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    My main gig is in the classroom :)

  • @lindaren9467
    @lindaren94673 жыл бұрын

    I have been struggling with my stat studies over a week now and so grateful for all your videos and they really help me a great deal. So amazing how you can make complicated things so simple and understandable. Also nice to watch your videos without having to experience annoying commercials. Thanks!

  • @lelelanaa2500
    @lelelanaa25009 жыл бұрын

    Whenever I have to watch Stats videos...always check for this channel first!!! Best channel for Statistics!! Would recommend to anyone!

  • @angelachanel9503
    @angelachanel95034 жыл бұрын

    almost 8 years later.. and I also think this is brilliant! Thank you!

  • @MissSilanda
    @MissSilanda8 жыл бұрын

    If my professor explained it this well I wouldn't be here.. Thank you so much😀👌 it makes much more sense now💃

  • @leneescott
    @leneescott7 жыл бұрын

    You saved my life! I am taking Statistics online this semester so I have to learn everything on my own. But I was never one from learning straight from a book. I was so confused and getting frustrated. This video is a life saver! Thank you!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome. I'm glad I could help!

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    The expected value is just the mean, which is given in the video (the midpoint between the minimum and maximum). To use calculus to show that, you would find the definite integral of x*1/(d-c) dx, between c and d.

  • @rahulvarma7257
    @rahulvarma72574 жыл бұрын

    wonderful explanation sir. you’re way of teaching is very much comfortable even for average students. keep it up 👏👏

  • @saikrishna2000
    @saikrishna20005 жыл бұрын

    Your channel is just awesome! You clearly explain each and every concept, and am happy for that. You just gained another sub. Cheers!

  • @rasikmohamed500
    @rasikmohamed5002 жыл бұрын

    Woww..Short and crispy..Watching this 9years old video for my Data science introductory....Maths have no versions..Big Thanks to god ❤️

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    I'm glad to be of help! I tried to build them to last the test of time.

  • @tlhomotsemoteme2423
    @tlhomotsemoteme24236 жыл бұрын

    Thank you so much, I really appreciate your work. I understand better than before when I watch your videos. Thank you.

  • @goodknight3072
    @goodknight30724 жыл бұрын

    My teacher used some terrible quality video for gamma and exponential distributions. I was wondering why until I noticed you didn't have a video on it (atleast that I could find). So glad to be back watching your videos again. Thanks again for teaching me stats!

  • @shareemrasyidi9948
    @shareemrasyidi99483 жыл бұрын

    Iam really struggling hard on statistics because of online class being very ineffective, glad this channel can really explain it pretty well and easy to understand

  • @abercrombie4ever100
    @abercrombie4ever1004 жыл бұрын

    I am beyond grateful for your stats videos! THANK YOU VERY MUCH!

  • @abdullahshahid9051
    @abdullahshahid90512 жыл бұрын

    What i like about your videos are that they focus on understanding and intuition; not tricks on how to compute. Great job!

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    Thanks so much! I'm always happy to hear this type of compliment as that's what I always shoot for. I teach statistics here, not tricks and tips for answering statistics questions.

  • @Akshay-lj4fh
    @Akshay-lj4fh6 жыл бұрын

    Great job!!! Very useful videos.. I was panicking till now; I open this channel and keep watching videos in loop and I find that I am done!!!! Superb!!!!!!

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    I'm glad you found my videos helpful!

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    The 20th percentile is the value of the variable that yields an area to the left of 0.20. The area to the left is the area of a rectangle with a base of a - 200, and a height of f(x). This means that (a-200)f(x) = 0.20. (d-c)f(x) = 1, since d and c are given as the endpoints.

  • @christinenalwoga6008
    @christinenalwoga60083 жыл бұрын

    Wow, your work is really of much help than you could even imagine

  • @jimmybandme
    @jimmybandme8 жыл бұрын

    Great job man, tons of respect for you. Thank you for helping all of us non-stats kids out, keep up the amazing job :)

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +jimmybandme You are very welcome, and thanks for the compliment!

  • @mustahidhasan5098
    @mustahidhasan50985 жыл бұрын

    Thanks for your lecture.That seems these videos were made 7 years ago when i was just a kid, but still helpful for me in this stage.Again thank u for clearing the basic concept

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks for the kind words, and I'm very glad I could help. I built them to stand the test of time :) The basic concepts of statistics and the underlying mathematics stay the same of course, but I also chose examples that would't look out of place 50 years from now.

  • @tahamagdy4932
    @tahamagdy49327 жыл бұрын

    Just saved my life. I would give you a hug.

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    I would take one! I'm glad to be of help.

  • @jbstatistics
    @jbstatistics10 жыл бұрын

    You're very welcome Kary! Je t'en prie!

  • @60daan
    @60daan4 жыл бұрын

    Thanks! learned more in this video than in an entire lecture from my "teacher" !

  • @rehabmadkhali6649
    @rehabmadkhali66499 жыл бұрын

    it's so clear to understand ....thank you

  • @0301850
    @030185011 жыл бұрын

    Best video i've ever watched for the uniform distribution

  • @ishanpandey4300
    @ishanpandey43005 жыл бұрын

    This was honestly so useful. I was going crazy over this. Thank you so much :)

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome.

  • @sharminmanocha3938
    @sharminmanocha39384 жыл бұрын

    This helped me understand so much better, thank you !!

  • @jbstatistics
    @jbstatistics10 жыл бұрын

    You are very welcome Jubayer.

  • @nernaykumar8334
    @nernaykumar83343 жыл бұрын

    One of the best explanations !!!!

  • @maurogg9682
    @maurogg96828 жыл бұрын

    Great Job .These video series are awesome . Very well explained and expose . Thanks a lot men

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    Thanks!

  • @kinleyyangzom5318
    @kinleyyangzom53188 жыл бұрын

    thank you!! all the videos i watched of yours' were very helpful!!!

  • @DarkZoneGamingMain
    @DarkZoneGamingMain10 жыл бұрын

    Your videos helped me immensely man, I can't thank you enough! I have done all my practice questions for the entire year but there is one type of question I can wrap around, its slightly different in its format don't know if you could take a look at it: Consider a uniform distribution between 0 and b where b is unknown, i.e. x~ U(0, b) i) A single sample is observed with value x=5.0. What is the maximum likelihood (ML) estimate for the parameter b? How would this type of question be done? Im not sure what is maximum likelihood..

  • @angie9zhou
    @angie9zhou4 жыл бұрын

    easy to understand. easy sample. good job. hope to see the normal distribution video

  • @smartcupoftea8972
    @smartcupoftea89726 жыл бұрын

    Very well done. Easy to understand and easy to follow. Thank you!

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!

  • @markgao5963
    @markgao59637 жыл бұрын

    When it comes to the night before my pstat final.

  • @DaanTheodenPro

    @DaanTheodenPro

    6 жыл бұрын

    Did you make it?

  • @marietouakeita

    @marietouakeita

    5 жыл бұрын

    How did you do?

  • @christophergonzalez1464

    @christophergonzalez1464

    5 жыл бұрын

    im curious as well

  • @revl6151

    @revl6151

    3 жыл бұрын

    Did you fail?

  • @markgao5963

    @markgao5963

    3 жыл бұрын

    @@revl6151 lol I passed it and graduated last year.

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    Yikes! Thanks for letting me know -- I hadn't noticed that. I'll have to fix that up.

  • @duytran-hg4cl
    @duytran-hg4cl4 жыл бұрын

    thank u so much, it still works until today !

  • @mohammedyousri5826
    @mohammedyousri58264 жыл бұрын

    very good explanation do not stop

  • @abdallahgamal5092
    @abdallahgamal50926 жыл бұрын

    Your videos are amazing i hope you continue them by making videos for the joint disturbutions and the covariance and the correlations thank you so much

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    Thanks for the compliment! I'll be making new videos in the new year, and will try to get to your suggestions (they are commonly suggested topics). All the best.

  • @kushaleshshetty
    @kushaleshshetty2 жыл бұрын

    Thank you so much for this excellent video..

  • @samikshamallaiya2924
    @samikshamallaiya29242 жыл бұрын

    nicely well explained.thank you so much

  • @ignantxxxninja
    @ignantxxxninja2 жыл бұрын

    concise and great explanation

  • @shridz_
    @shridz_2 жыл бұрын

    Your videos are brief and to the point. I really love them. However I want to point out something. I believe that for x in (c,d), the values c and d are not inclusive, hence we should write c This is also because the c.d.f. of X is not differentiable at points x = c and x=d so the p.d.f. f(x) doesn't exist at these points.

  • @shreyashankar6773
    @shreyashankar67738 жыл бұрын

    this is brilliant, thank-you so very much

  • @jideenitan
    @jideenitan3 жыл бұрын

    Thank you so much. I've learned so much on probability distribution thank to you.

  • @jbstatistics

    @jbstatistics

    3 жыл бұрын

    I'm glad to be of help!

  • @LiveLoveLifewithRima
    @LiveLoveLifewithRima5 жыл бұрын

    It's so clear to understand. Thank you

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome!

  • @Kevin-cy2dr
    @Kevin-cy2dr4 жыл бұрын

    Is your statistics course enough for data science/machine learning?

  • @MisterBinx
    @MisterBinx3 жыл бұрын

    OMG why is this so simple here. I was thinking something completely different.

  • @jmoney9439
    @jmoney94394 жыл бұрын

    So how do you know that u need to take the left side area or the right side?

  • @psudhir4336
    @psudhir43364 жыл бұрын

    Excellent explanation, but one thing, you could have shown the equivalent way of doing with integration too i.e integration of f(x) dx with limits 230 to 250, many places I see the f(x) as 1 for uniform distribution ..how that rho(x) is calulated

  • @DarrellBarnes
    @DarrellBarnes5 жыл бұрын

    Broken down for a simple guy like me....thanks!

  • @bijoudeaux1
    @bijoudeaux111 жыл бұрын

    Another great video but I don't understand why for the percentile part you used: (a-200) * 1/50= 0.2. According to the info, the formula is d-c * f(x). In this case, why didn't you use 250 as d and the other c. That's where I am confused.

  • @DbzFighter02
    @DbzFighter0211 жыл бұрын

    is there an expected value when using a uniform distribution

  • @kingsleyking6690
    @kingsleyking66909 жыл бұрын

    can the interval be negactive? e.g -1=1

  • @ICOD73
    @ICOD739 жыл бұрын

    Thx for this clear explanation but I am wondering why you didn't mention the moment generating function also. It is useful in finding the mean and variance.

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    To this point, my videos have been pitched at the level of an applied statistics course to students not majoring in statistics. While moment generating functions are certainly useful, they are not something that is typically discussed in this type of introductory statistics course. Cheers.

  • @leetran7123
    @leetran71232 жыл бұрын

    Thank you very much, very helpful for me!

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    You are very welcome! I'm glad to be of help!

  • @leandronapalinga536
    @leandronapalinga53610 жыл бұрын

    do you have a video of the discrete uniform distribution?

  • @antisocialbarbie1587
    @antisocialbarbie1587 Жыл бұрын

    May the almighty bless you thank you so much

  • @vansikasingh3228
    @vansikasingh32283 жыл бұрын

    Thank you so much!

  • @olgaromazan5894
    @olgaromazan58946 жыл бұрын

    excellent explanation. thanks

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome!

  • @hesahesa5665
    @hesahesa56657 жыл бұрын

    شكرا لك افضل فيديو شفته thanks very much

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome!

  • @anvin5251
    @anvin525110 жыл бұрын

    V good explanation. Thanks a ton!

  • @jbstatistics

    @jbstatistics

    10 жыл бұрын

    You are very welcome!

  • @cemturanl250
    @cemturanl2507 жыл бұрын

    Man you are great thank you very much

  • @Hellstorm79
    @Hellstorm7911 жыл бұрын

    This is an awesome video, super helpful. Right up until the percentile part. That needs to be greatly clarified. How you actually got the .2 is not clear at all.

  • @orkhanhasanov1922
    @orkhanhasanov19222 жыл бұрын

    Perfdct explanation!

  • @IggyOVOXO
    @IggyOVOXO7 жыл бұрын

    You are the real MVP

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Sometimes, yes I am!

  • @satoseitoku
    @satoseitoku2 жыл бұрын

    Nice video!

  • @bijoudeaux1
    @bijoudeaux111 жыл бұрын

    I looked at it again and was able to understand. (Y)

  • @str223
    @str2234 жыл бұрын

    Thank you Sir.

  • @GOODBOY-vt1cf
    @GOODBOY-vt1cf4 жыл бұрын

    thank you so much

  • @ryans.6273
    @ryans.62735 жыл бұрын

    My college stats professor is goddamn useless. Thanks for this

  • @TheDekramer

    @TheDekramer

    3 жыл бұрын

    i think were in the same boat lmao

  • @afaf6478
    @afaf64787 жыл бұрын

    thanks! great explanation

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Thanks for the compliment!

  • @arlettemunoz3639
    @arlettemunoz36394 жыл бұрын

    what does f(x) represent in the context of a problem??

  • @raggihosni4030
    @raggihosni40305 жыл бұрын

    god bless you dude again!

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks!

  • @josebernardosanchezetchega501
    @josebernardosanchezetchega5019 жыл бұрын

    The best channel to learn statistics! Thanks man!

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    You are very welcome. Thanks for the compliment!

  • @josebernardosanchezetchega501

    @josebernardosanchezetchega501

    9 жыл бұрын

    :D thanks to you I'll ace my next stats test keep the good work !

  • @Brownlee314
    @Brownlee31411 жыл бұрын

    Nice video!! (except that part in the percentile example where you wrote 0.2 = 210)

  • @dawsonschwatz4102
    @dawsonschwatz41025 жыл бұрын

    He explains it so well, this video is saving my ass right now 😂

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    I'm glad to be of help!

  • @hamoody3
    @hamoody37 жыл бұрын

    20th percentile. why to the left not the right. Why a-200 not a-250?

  • @SB_Roy_Vlogs
    @SB_Roy_Vlogs Жыл бұрын

    wow...excellent

  • @yashjain1695
    @yashjain16958 ай бұрын

    Question: for P(X>230) shouldnt it be 250-231 and not 230 since the minimum value x can take on is 231

  • @jbstatistics

    @jbstatistics

    8 ай бұрын

    It's a continuous distribution. P(X > 230) = P(X > 230.0000000000000000000000000...) In the example, X doesn't take on only whole number values, it takes on any value in the continuum between 200 and 250.

  • @em5506
    @em55064 жыл бұрын

    Thank You!!

  • @ollod
    @ollod6 жыл бұрын

    I have a problem of concept here. If the probability of getting f(x) = 1/50 for 200

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    This video discusses the *continuous* uniform distribution, where the random variable can take on an infinite number of possible values. You're thinking of a discrete uniform distribution, with 51 equally likely possibilities, but that's not the case here.

  • @nuhabinganem2854
    @nuhabinganem285410 жыл бұрын

    I should say thank you because its amazing explanation thank you so much

  • @m.l.f.rilwana
    @m.l.f.rilwana3 жыл бұрын

    I have a question what if a is negative and b is positive value When applying to equation do I disregard the sign?

  • @jbstatistics

    @jbstatistics

    3 жыл бұрын

    No, leave the sign in. There are no issues with a being negative (or a and b being negative). The only restriction is that b > a.

  • @m.l.f.rilwana

    @m.l.f.rilwana

    3 жыл бұрын

    Ok thankyou

  • @karyho7399
    @karyho739910 жыл бұрын

    Thank u so much!! Merci

  • @Kushagra_Gupta
    @Kushagra_Gupta4 жыл бұрын

    what if c =0,d=1 then 1/(c-d) would be equal to 1 for every number

  • @jlahmed
    @jlahmed10 жыл бұрын

    Thank you

  • @sethasmah5407
    @sethasmah54073 жыл бұрын

    THANKS SIR

  • @mankmerohit
    @mankmerohit2 жыл бұрын

    Excellent u r genius

  • @Rahul-oq7wc
    @Rahul-oq7wc6 жыл бұрын

    taking value of (b-a)1 don’t that contradict f(x) RANGE?

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    For continuous distributions, the restrictions on f(x) are: 1) f(x) >= 0 everywhere, and 2) f(x) integrates to 1. The value of f(x) can be (and often is) greater than 1. This is not a problem, as the value of f(x) is not itself a probability, but is simply the height of the curve at point x.

  • @Rahul-oq7wc

    @Rahul-oq7wc

    6 жыл бұрын

    thanks for the instant reply and correct me

  • @rugvedkulkarni1593
    @rugvedkulkarni15933 жыл бұрын

    What happens when you are looking for Greater than and including or lesser than and including a certain point?

  • @jbstatistics

    @jbstatistics

    3 жыл бұрын

    If X is any continuous random variable, and b is any constant, then P(X=b) = 0, and thus P(X>=b) = P(X > b) and P(X

  • @rugvedkulkarni1593

    @rugvedkulkarni1593

    3 жыл бұрын

    @@jbstatistics Thank you! This helped me a lot! :)

  • @muratcan__22
    @muratcan__225 жыл бұрын

    Right choice for all the distribution types

  • @muratcan__22

    @muratcan__22

    5 жыл бұрын

    There are some minor things that makes these videos special. For example when you say it is not a distribution unless we write the Random variables Xs and the probabilities. That sentence solidify the term distribution in minds of students like me who are just memorized the distrubition word but have never got the intuition of it

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    Thanks so much for the kind words! I'm very happy that my methods help you develop a better intuitive understanding of the topics!

  • @karimkhan1312
    @karimkhan13128 жыл бұрын

    thank u sir

  • @bicepjai
    @bicepjai9 жыл бұрын

    good job

  • @Once-Upon-A-Dime
    @Once-Upon-A-Dime6 жыл бұрын

    Hello Professor, if the median and mean is 50% of the distribution, the formula should be (a-200)x1/50 = 50/100 *not* c+d/2 because 0 to C is least of the concern, I think it should be (d-c)/2... If you have time, please guide.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    For the example in this video, the mean and median would lie halfway between 200 and 250. Solving for a in (a-200)*1/50 = 50/100 yields a = 225, and (200 + 250)/2 = 225. Either way we get the same (correct) result. (d-c)/2 = 25, which is the *distance* from either endpoint to the median, but is not the median.

  • @Once-Upon-A-Dime

    @Once-Upon-A-Dime

    6 жыл бұрын

    jbstatistics Thank you sire, sorry to disturb for my silly calculation error.

  • @yap9660
    @yap96604 жыл бұрын

    Why the area is equal to 1?

  • @josephinemwidya
    @josephinemwidya6 жыл бұрын

    Thank you!

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    You are very welcome!