An Introduction to the Continuous Uniform Distribution
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- Опубліковано 6 жов 2024
- 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... .)
I never comment on anything, but this is so excellent. Immediately understood a concept I have been trying to understand for twelve hours.
I'm glad to be of help!
You and me both! This makes SO much sense when explained properly
Do you get the logic of formula of Variance?
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.
Good instructors are usually found on UA-cam and not in classrooms! Thanks!
My main gig is in the classroom :)
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.
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.
I have a professor that truly doesn’t understand the profession and subject he has selected. His poor choice has me searching through UA-cam 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!
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!
You are very welcome. I'm glad I could help!
almost 8 years later.. and I also think this is brilliant! Thank you!
Whenever I have to watch Stats videos...always check for this channel first!!! Best channel for Statistics!! Would recommend to anyone!
If my professor explained it this well I wouldn't be here.. Thank you so much😀👌 it makes much more sense now💃
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
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.
What i like about your videos are that they focus on understanding and intuition; not tricks on how to compute. Great job!
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.
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!
Woww..Short and crispy..Watching this 9years old video for my Data science introductory....Maths have no versions..Big Thanks to god ❤️
I'm glad to be of help! I tried to build them to last the test of time.
wonderful explanation sir. you’re way of teaching is very much comfortable even for average students. keep it up 👏👏
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
Just saved my life.
I would give you a hug.
I would take one! I'm glad to be of help.
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!!!!!!
I'm glad you found my videos helpful!
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!
You're very welcome Kary! Je t'en prie!
When it comes to the night before my pstat final.
Did you make it?
How did you do?
im curious as well
Did you fail?
@@revl6151 lol I passed it and graduated last year.
Great job man, tons of respect for you. Thank you for helping all of us non-stats kids out, keep up the amazing job :)
+jimmybandme You are very welcome, and thanks for the compliment!
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 < x < d.
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.
it's so clear to understand ....thank you
Thanks! learned more in this video than in an entire lecture from my "teacher" !
Wow, your work is really of much help than you could even imagine
You are very welcome Jubayer.
Thank you so much, I really appreciate your work. I understand better than before when I watch your videos. Thank you.
Yikes! Thanks for letting me know -- I hadn't noticed that. I'll have to fix that up.
I am beyond grateful for your stats videos! THANK YOU VERY MUCH!
easy to understand. easy sample. good job. hope to see the normal distribution video
Best video i've ever watched for the uniform distribution
Your channel is just awesome! You clearly explain each and every concept, and am happy for that. You just gained another sub. Cheers!
Great Job .These video series are awesome . Very well explained and expose . Thanks a lot men
Thanks!
One of the best explanations !!!!
This was honestly so useful. I was going crazy over this. Thank you so much :)
You are very welcome.
OMG why is this so simple here. I was thinking something completely different.
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
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.
Very well done. Easy to understand and easy to follow. Thank you!
You are very welcome!
thank u so much, it still works until today !
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.
Broken down for a simple guy like me....thanks!
This helped me understand so much better, thank you !!
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.
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.
Thank you so much.
I've learned so much on probability distribution thank to you.
I'm glad to be of help!
very good explanation
do not stop
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
thank you!! all the videos i watched of yours' were very helpful!!!
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..
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.
The best channel to learn statistics! Thanks man!
You are very welcome. Thanks for the compliment!
:D thanks to you I'll ace my next stats test keep the good work !
It's so clear to understand. Thank you
You are very welcome!
Thanks for the video, i believe 6:51 is mathematically incorrect bij saying 0.2=210
nicely well explained.thank you so much
Nice video!! (except that part in the percentile example where you wrote 0.2 = 210)
Thank you so much for this excellent video..
At 6:27 minutes you claim that 0.2 is equal to 210!!!! Please, make a correction; just add another line saying a = 200 + 0.2x50 = 210.
Thank you very much, very helpful for me!
You are very welcome! I'm glad to be of help!
My college stats professor is goddamn useless. Thanks for this
i think were in the same boat lmao
Right choice for all the distribution types
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
Thanks so much for the kind words! I'm very happy that my methods help you develop a better intuitive understanding of the topics!
Why are the random people on the internet so much better at teaching concepts than people who have trained for atleast 4 years to do exactly that?
Is your statistics course enough for data science/machine learning?
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.
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.
jbstatistics Thank you sire, sorry to disturb for my silly calculation error.
Hey man, you've got an error when you loosely used the equal sign. You should separately say a = 210 instead.
Yes, thanks for pointing that out. Had a brain fart there. I've addressed that in the comments, and created an updated version without the error. I put in an annotation fix long ago, but I don't know if those things show up anymore.
20th percentile. why to the left not the right. Why a-200 not a-250?
this is brilliant, thank-you so very much
May the almighty bless you thank you so much
is there an expected value when using a uniform distribution
what if c =0,d=1 then 1/(c-d) would be equal to 1 for every number
So how do you know that u need to take the left side area or the right side?
I have a problem of concept here. If the probability of getting f(x) = 1/50 for 200
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.
You are the real MVP
Sometimes, yes I am!
Question: for P(X>230) shouldnt it be 250-231 and not 230 since the minimum value x can take on is 231
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.
excellent explanation. thanks
You are very welcome!
taking value of (b-a)1 don’t that contradict f(x) RANGE?
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.
thanks for the instant reply and correct me
do you have a video of the discrete uniform distribution?
what does f(x) represent in the context of a problem??
I looked at it again and was able to understand. (Y)
What happens when you are looking for Greater than and including or lesser than and including a certain point?
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
@@jbstatistics Thank you! This helped me a lot! :)
can the interval be negactive? e.g -1=1
thank you so much
Why the area is equal to 1?
why in variance we divide by 12 this is unclear.
شكرا لك افضل فيديو شفته
thanks very much
You are very welcome!
He explains it so well, this video is saving my ass right now 😂
I'm glad to be of help!
I should say thank you because its amazing explanation
thank you so much
Huh. Shouldn't this be taught before Normal Distribution?
Yes, it's typically best to discuss this simple distribution before the normal distribution. Why the "huh"?
thanks! great explanation
Thanks for the compliment!
V good explanation. Thanks a ton!
You are very welcome!
intuitively, what does f(x) actually mean?
There's no super easy and understandable explanation to that. The value of f(x) at x is the rate of change of the cumulative distribution function F(x) at x. Probably the easiest explanation is the rectangle approximation to the integral: for a small change in x (delta x, say), f(x)*delta x is approximately P(x < X < x + delta x).
I have a question what if a is negative and b is positive value
When applying to equation do I disregard the sign?
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.
Ok thankyou
god bless you dude again!
Thanks!
Man you are great thank you very much
Thank you Sir.
Nice video!
Thank you so much!
Perfdct explanation!
Thank You!!
4 people already failed
wow...excellent