Probability Density Function of the Normal Distribution

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  • Опубликовано: 22 дек 2024

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  • @roccellarocks
    @roccellarocks 4 года назад +125

    Have never had anyone in my entire student career that explained math with such clarity and passion. I have been seeing this entire video at half past midnight and this felt interesting, not frustrating!

  • @wesleydupreez2909
    @wesleydupreez2909 Год назад +12

    Never in all my life, has a teacher explained mathematics in this way. The "adding" of different rules to augment the behaviour of the graph is so helpful for students who want to understand the REASON for the behaviour.

    • @Dergicetea
      @Dergicetea 7 месяцев назад

      I agree with you, sir. This was quite illustrative to watch.

  • @vinyasshreedhar9833
    @vinyasshreedhar9833 3 года назад +29

    If only I had a teacher like Eddie Woo, I would have certainly taken Maths as my honours. When I first looked at the PDF of normal distribution, I fainted thinking its only people at PhD maths level could decipher. Now it makes sense how it came into picture so easily. I am a huge fan of Eddie😊

  • @paulbrown5839
    @paulbrown5839 4 года назад +3

    You Aussies are very lucky to have a teacher like Eddie Woo

  • @sibusiso2070
    @sibusiso2070 4 года назад +10

    The Normal distribution equation was really daunting at first but you really clarified and derived well and simplified things a whole lot more. Thank you so much.

  • @inexteducation5393
    @inexteducation5393 2 года назад +2

    13:08, Sir Eddie said, it is not an exclamation sign but a mathematical notation, okay! It's called Factorial.
    I laughed so goddamn hard! You are really AN AMAZING TEACHER! LOVE YOU MAN!

  • @tonnynyaoke1794
    @tonnynyaoke1794 2 года назад

    I feel lucky I came across Woos content, this is just a life saviour. So simple.

  • @dalipmudhar4107
    @dalipmudhar4107 4 года назад +7

    Omg I have an applied test this week and this just came in clutch. Tsym Eddie.

  • @fullduckdev7327
    @fullduckdev7327 2 года назад +1

    Hands down the best teacher ever :)

  • @TILearningCentre
    @TILearningCentre 4 года назад +11

    Eddie - At 1:25 you eliminate trigonometric functions (no horizontal asymptote), but arctan(x) has a horizontal asymptote. Graph the function pi/2-arctan(x^2) and you get something that looks remarkably similar to the normal distribution. If you include a dilation of 1/(pi.root(2)) the function has a definite integral of 1 over the domain (-infinity, + infinity). Now you will need to graph it against the "normal" distribution to see that it is actually different.
    Now consider the graph of 1/n - 1/n tanh(x^2/n) and you get something even better. Of course this might be thought of as cheating since the tanh(x) is related to e^x ... and hence why we cannot eliminate trigonometric functions from the mix so easily.

  • @alizarind1852
    @alizarind1852 2 года назад

    I wish i had any teacher like you in my life. How passionate seem.

  • @shillowcollins6392
    @shillowcollins6392 Год назад

    the best teacher ever, you earned a new subscriber. wow, I am super impressed

  • @sagarikabiswas1534
    @sagarikabiswas1534 2 года назад

    OMG wow! I never in my life knew that this could be traced down in this way. Thank you so much.

  • @pratibhas2468
    @pratibhas2468 Год назад +1

    I just don't have words to express how exceptional your style of teaching is... Never had a teacher this passionate who sort of untangles all the complicated stuff step by step in an orderly way so that students can actually understand the concept. Thank you so much sir! I really really appreciate the effort you put in.. 🙏🏻🙏🏻 You might never see this but I just couldn't help but say it 🥰🥰

  • @vanshikasinghal4948
    @vanshikasinghal4948 3 года назад +1

    I wish I had teachers like him. These kids are literally so lucky

  • @sreyag4766
    @sreyag4766 7 месяцев назад +1

    OMG!!! such a neat and crisp explanation!! Thanks sir!

  • @samiswilf
    @samiswilf Год назад

    This professor is top class.

  • @nicolasflores6046
    @nicolasflores6046 4 года назад +3

    One of the best math videos on youtube hands down 🔥

  • @danielsoares7456
    @danielsoares7456 3 года назад

    Its really blew my mind, you made Gaussian standard distribution something easy to understend, thats the thing, thx!

  • @Jacked_R_Us
    @Jacked_R_Us 4 года назад +1

    Honestly Eddie you explain everything so well

  • @juancer_
    @juancer_ 4 года назад +4

    wow is incredible how much out educational systems differs each other, I know what a factorial is but I have never studied the normal distribution... thanks!!

  • @finalpurez
    @finalpurez 2 года назад

    The way he explained it is so good!

  • @harunduman8529
    @harunduman8529 2 года назад

    Man, you are a great teacher.

  • @fredericoamigo
    @fredericoamigo 2 года назад

    Seriously dude, I really appreciate your videos. I like your teaching style and way of communicating things. Keep up the good work! Cheers.

  • @lizaminasyan9255
    @lizaminasyan9255 3 года назад +1

    i wish i had a teacher like u! u made me so interested in this!

  • @rmcgraw7943
    @rmcgraw7943 9 месяцев назад

    U R a good teacher. U explain it such that I can UNDERSTAND it, not replicate it from memory. With such knowledge, I can derive usage of this in other theoretical applications. Most people memorize, but I don’t ever remember it unless I UNDERSTAND its applicability. Thanks. I want to learn more about the CDF and how you arrive at it using the PDF. I think you’re going to use an area under the curve, but am not sure.

  • @metahomset9906
    @metahomset9906 3 года назад

    Perfect way to do my revision as I prepare for end of semester exam... inspirational

  • @didarislam1900
    @didarislam1900 2 года назад

    I was so impressed! Great job Eddie! It would've been nicer if the students could keep quiet for a while! Great job!

  • @charlesnorvow
    @charlesnorvow 3 года назад

    What is the next part of this video? Jesus! this is so good! Thanks, Prof. Woo

  • @imotvoksim
    @imotvoksim 11 месяцев назад

    I LOVED EVERY SECOND OF THIS!!!!

  • @ishrakbenali743
    @ishrakbenali743 Год назад

    this men is a legend!

  • @goldenonlypresenttime3697
    @goldenonlypresenttime3697 4 года назад

    I can't believe Iam watching all his fantastic explanations for long hours he is best

  • @papafreddy2123
    @papafreddy2123 2 года назад +1

    If you're watching this and are interested in knowing where the cumulative distribution function comes from, it's the integral of the Maclaurin series expansion of e^-1/2z^2 centred at z=0. Don't know what that means? Google search or search on RUclips "Maclaurin series" and it'll make a lot more sense why it looks the way it does.

    • @carultch
      @carultch 2 года назад

      I prefer the term Taylor Series, because it is a polynomial that is TAILORED to match the behavior of the function, by matching every order of derivative at one point.

  • @Subramanyam_J
    @Subramanyam_J 3 года назад

    Thanks Eddie.. one of the best explanations I found.

  • @AwaisKhan-mh6cd
    @AwaisKhan-mh6cd 3 года назад

    These kids are the luckiest people on earth. If he was my Math teacher i would have become a Mathematician

  • @thomasstern6814
    @thomasstern6814 Год назад

    just wow, wonderful video. Thank you!

  • @Amine-gz7gq
    @Amine-gz7gq 2 года назад

    I love this teacher even though I'm not a student anymore (I'm 32 but still trying to better visualize what I already know).

  • @goldenonlypresenttime3697
    @goldenonlypresenttime3697 4 года назад

    You are best because of you my interest and love for maths is growing it's getting stronger and probably physics also becoming strong thanks a lot

  • @PowerhouseCell
    @PowerhouseCell 4 года назад +38

    WOAH this was explained beautifully. I've never had anyone derive the normal distribution function like that, it actually makes so much sense :o
    By the way, I have to wonder... What level of math does he teach? Because he's explaining rather difficult topics such as z-scores, PDFs, and integration, but his students don't know what a factorial is? Pretty interesting to say the least

    • @ShadowViewsOnly
      @ShadowViewsOnly 4 года назад +1

      AFAIK these are 12th grade high school students.
      I was also weirded out by the fact that some of his videos are explaining elementary school stuff, like area of a triangle, then comes this... :D

    • @biubiu9356
      @biubiu9356 4 года назад +2

      He is a high school teacher. He teaches 2u (advance) math for year 12 this year in NSW. He also teaches from year 7 to year 12 like other high math school teachers do. I’m a current year 12 student. But I actually wonder how his school allows him to teach 2u instead of 4u math. He is a fantastical teacher!!!

    • @EhsaanHossain
      @EhsaanHossain 4 года назад +10

      He did a little bit of math misdirection there: he made you pay attention to exponential functions, when really a lot more going on --- but he swept the other details under the rug.
      Like what about y = 1/(1+x^2)? There's a rational function with no vertical asymptotes, and its graph looks just like the normal distribution. He didn't explain why statisticians don't use this function instead of exponential (hint: integrals). He glossed too quick over the rational functions, but yes it was convincing if you're not looking closely :)

    • @timandersen8030
      @timandersen8030 4 года назад +4

      That wasn't a derivation. It's just simplification. He doesn't even tell what the 2pi is there for. It's a shame. Advanced students could use an excellent teacher too, not just high school kids.

    • @peacecop
      @peacecop 4 года назад +1

      @@biubiu9356 What do you mean by "2u" and "4u"?

  • @anushgopalakrishnan
    @anushgopalakrishnan 4 года назад +49

    what kind of class is there where they know what integrals are but don't know what factorials are?

    • @LJohann
      @LJohann 4 года назад +1

      Ye no clue im sitting the same syllabus as them and i cant believe they dont know

    • @davidwright8432
      @davidwright8432 3 года назад +9

      At lest one person didn't. conclude nothing on sample sizes of one!

    • @izzyheslop7522
      @izzyheslop7522 3 года назад +6

      In Australia integrals are a part of the advanced course but factorials are only done in extension :)

    • @sppss914
      @sppss914 3 года назад

      yh I was confused too lol.

    • @yuriperez1221
      @yuriperez1221 3 года назад

      i think the class is staged.

  • @tracysara6754
    @tracysara6754 Год назад

    An active class🙌👏👏

  • @CanDoSo_org
    @CanDoSo_org 2 года назад

    You are a genius. Thanks.

  • @crayon_sunset
    @crayon_sunset 2 года назад

    wonderful teaching! wish i had you as my statistics teacher

  • @abhilashkokkonda1713
    @abhilashkokkonda1713 3 года назад

    That's an outstanding explanation

  • @maricellahwanjiku9704
    @maricellahwanjiku9704 Год назад

    Very lively class💞✨

  • @rahuldevgun8703
    @rahuldevgun8703 7 месяцев назад

    Just Beautiful and WOW

  • @nasimulislam4067
    @nasimulislam4067 3 года назад

    wish i had a teacher like him

  • @ihgnmah
    @ihgnmah 3 года назад

    Damn, now I'm gonna remember this equation forever!

  • @ankursharma2775
    @ankursharma2775 Год назад

    Best explaination of PDF

  • @taneledlamini9505
    @taneledlamini9505 3 года назад

    Very clear, thank you so much.

  • @alexvorabouth5320
    @alexvorabouth5320 2 года назад

    Love this!

  • @SportsManVegetal
    @SportsManVegetal 2 месяца назад

    Eddie, please explain how the CDF is derived. Very interested.

  • @lizaminasyan9255
    @lizaminasyan9255 3 года назад

    thank you for your efforts

  • @vinodwadhwani9330
    @vinodwadhwani9330 3 года назад

    professor eddie woo is so underrated

  • @alecmacartney2807
    @alecmacartney2807 Год назад

    saving my life atm

  • @dimple3428
    @dimple3428 3 года назад +1

    the best part of this vedio is when eddie brings the upside down parabola onto the screen & everyone is awestruck,,is pretty good right😍

  • @ChaseyMih
    @ChaseyMih Год назад

    This is wholesome

  • @priscillalu2804
    @priscillalu2804 3 года назад

    Amazing!! THANK YOU!

  • @FINDNG1
    @FINDNG1 2 года назад

    Thank you

  • @mustafizurrahman5699
    @mustafizurrahman5699 2 года назад

    Mesmerising. Thank you very much sir for lucid explanation. Would you please explain about the coefficient (1/sigma^2. Sort (2pi). How did we get it

    • @Adam-wc4xm
      @Adam-wc4xm 2 года назад

      yes, please

    • @carultch
      @carultch 2 года назад

      The sqrt(2*pi) and sigma^2 come from "forcing" the function to have a total area under the curve of 1, since a probability density function must have a total integral of 1 for it to make sense for the application.
      If you integrate e^(-x^2) dx over all real numbers, which is called the Gaussian function, you will end up with sqrt(pi). To do this, you make a coordinate transform by squaring the function, and carrying out the integral in polar coordinates. You will integrate e^(-r^2)*r*dr*dtheta from r=0 to infinity, and theta = 0 to 2*pi. Doing this, allows us to perform integration by substitution, to make sense of this function that can't be integrated in closed-form. The variables of integration switch from dx * dy to r*dr*dtheta, and the r in this term becomes just what our integration method was asking for, so it could be possible to solve. This works well for finding the grand total area, but unfortunately, intermediate ranges cannot be integrated in closed form. We end up using a Taylor series of this function to define erf(x) and erfc(x) as the integral of it, so the distribution function can be integrated.
      In order for it to have a standard deviation equal to 1, when sigma is set to 1, we make another adjustment to the coefficient. Carry out the calculus that determines the variance on (1/sqrt(pi))*e^(-x^2), and we end up with a variance of 1/2, implying a standard deviation of 1/sqrt(2). To correct for this, sqrt(2) gets inserted into the denominator, and 1/2 gets inserted into the exponent.
      This gives us the standard normal in the form of:
      1/(sqrt(2*pi) * e^(-1/2*x^2)
      When we want to shift it laterally so it is centered on mu, we replace x with (x - mu).
      When we want to scale it laterally by sigma, we replace (x - mu) with (x - mu)/sigma.
      We then put sigma^2 in the denominator of the coefficient out in front, to "force" the area to equal 1.

  • @sabeteuwe
    @sabeteuwe Год назад

    6:16 shildnt mean as a plus?

  • @EliteNormie
    @EliteNormie Год назад

    damn i wanna know what happens on Thursday and Friday where's the video for that Mr Woo

  • @morancium
    @morancium 4 года назад +1

    can somebody explain why not Rational Functions?
    suppose a rational function whose denominator is non zero like 1/(1+x^2)
    please help

    • @randomblueguy
      @randomblueguy 4 года назад +2

      Integrals are easier to compute with exponentials, that’s why.

  • @YT-yt-yt-3
    @YT-yt-yt-3 2 года назад

    I regret I did not major in maths. Nevertheless I enjoy learning all these stuffs now. But I can guarantee if he had been my teacher, I would have choose a math track for sure.

  • @BlahBlahBlah13623
    @BlahBlahBlah13623 Месяц назад

    y=1/(x^2+1) hasnt got a vertical asymptote

  • @perseusgeorgiadis7821
    @perseusgeorgiadis7821 Год назад

    Why show the antiderivative of a function without an elementary antiderivative, using the Maclaurin series, to kids who have no idea what the Maclaurin series is...or, for that matter, the factorial

  • @theunknownscientist3249
    @theunknownscientist3249 4 года назад

    Hey, can someone help me start the stats videos? I don't really know where to begin. I really love your videos and I watched the whole complex number playlist, now I want to watch the statistics one, but I don't know where to start.

    • @dangitnicky
      @dangitnicky 4 года назад

      ruclips.net/p/PL5KkMZvBpo5C9nhzyacvNtcWHLh3mvXJE This should take you to where most of the probability/statistics videos should be. The topics are sorta all over the place video to video, so I really recommend watching these as a supplement to a Stat class.
      This playlist could be useful to you also ruclips.net/p/PL5KkMZvBpo5Bcz-V51UHtlg_eBW-PtQ7_

  • @reubengrice9836
    @reubengrice9836 4 года назад +2

    Anyone know where he teaches?

    • @dhruvsingh34
      @dhruvsingh34 4 года назад +1

      Sydney, Australia

    • @morancium
      @morancium 4 года назад

      @@dhruvsingh34 can you tell in which grade these students are??

    • @dhruvsingh34
      @dhruvsingh34 4 года назад +2

      @@morancium No Idea, Ashish.
      But he teaches at some High School.
      Check *About* of his RUclips Channel.

    • @LJohann
      @LJohann 4 года назад +1

      @@morancium year 12 im in yr 12 and we have to learn this

  • @muteguest60
    @muteguest60 3 года назад

    If he was my instructor i'd study math major for sure

  • @yechielh
    @yechielh 3 года назад

    brilliant

  • @jawadidrees1114
    @jawadidrees1114 3 года назад

    Great

  • @chariots
    @chariots 3 года назад

    well done

  • @davidwright8432
    @davidwright8432 3 года назад

    So that's where the Gaussian function comes from. I thought it was from Hell. Neener to Demons!

  • @quantumaravinth
    @quantumaravinth 3 года назад

    4 dislikes? I see.... Do those guys have functional eyes? or ears? I mean, Eddie Woo, you could only solve this puzzle :D

  • @aaronwtr1150
    @aaronwtr1150 4 года назад

    Do you share your slides somewhere? I’m a tutor helping students that have trouble with math and I would love to explain concepts using your slides. Thanks for making learning fun, you are the cornerstone of society!

  • @gaurav889
    @gaurav889 4 года назад +4

    They are talking so loud during the lec. He has some real patience while teaching.

    • @Zekbo
      @Zekbo 4 года назад

      Where

  • @xvgreen8586
    @xvgreen8586 Год назад

    Damn

  • @h0nk3d
    @h0nk3d 4 года назад +1

    POV: HSC is tmr

  • @musicsubicandcebu1774
    @musicsubicandcebu1774 4 года назад +1

    This comment is directed at Mr Woo, because of his comment on the importance of this function. But anyone interested in metaphysics is welcome to respond.
    Is the law of averages the most powerful force in the universe? This is a serious question - one which lead me to a simple explanation of several hitherto unexplained phenomena - such as the resistant idea of a God.

    • @randomblueguy
      @randomblueguy 4 года назад

      My take on the matter is that we find such patterns because our psychology evolved in such way, we’re not even sure if other intelligent life somewhere else in the universe possesses said abilities. Also, regardless of whether they’re intrinsic to the fundamental framework of the universe or not, invoking god here is an argument from ignorance which is a logical fallacy.

    • @joelagbo3862
      @joelagbo3862 4 года назад

      @@randomblueguy Colossians 2:3 IN Christ (GOD) are hidden all the treasures of Sophia(wisdom) and gnosis(Knowledge).

  • @minhhungle7488
    @minhhungle7488 3 дня назад

    ??? silly explanation
    x/sinh(x)
    1/cosh(x)
    (1+x^2/n)^-n
    they all look the same

  • @kushagratiwari7751
    @kushagratiwari7751 3 года назад

    Guys are studying normal distribution and don't know about factorials, I mean really??

  • @devashishjaiswal6037
    @devashishjaiswal6037 4 года назад +2

    I mean...the class does know that the video will end up on RUclips. Can't they just co-operate to save themselves some nasty judgment.