Uniform Distribution EXPLAINED with Examples

[@Tchoutchou_china]

🇩🇿I am an Arab, and I found your explanation of the lessons good and excellent. I thank you for your effort, Professor. Best regards, Be Algeria.

[@hilthaw2072]

You are my life saver. I asked my lecturer why the formula comes in this way and she fails to explain…. This saves everything and ignites my passion for learning again!

[@Johnson-l1r6x]

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[@thesoftwareguy2183]

While listening your lecture , I am feeling the concept , Thanks !!

[@AceTutors1]

I am so happy to hear that! Thanks for watching!

[@christopherbarrett9900]

You have a talent for teaching, congrats!

[@finncocoman3164]

Extremely underrated channel. You take concepts I find very challenging in class and make them very understandable. So far has been the greatest help in my uni stat class. Thank you guys!

[@AceTutors1]

That is an incredible compliment! Thank you for your support!

[@Kraykz]

this channel is such a life (time) saver

[@AceTutors1]

Thank you for your support! I'm glad we are able to help you out!

[@janaramon1232]

Dang it bro,this is the best and most simple video i could find on yt thanks G!

[@daanush468]

"You have big dreams, don't let a class get in the way". Aye aye, Captain!

[@AceTutors1]

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[@wc350]

That's exactly what I need to hear right now!

[@Randomrobo1817]

So true bro 😂

[@lililili2580]

I was so struggling with this, thank you for clear explanation )))

[@AceTutors1]

That's so great to hear! Thanks for sharing!

[@lindokuhleprecious9964]

So helpful and simple to understand🇿🇦Thank you

[@AceTutors1]

I'm glad you found this video helpful! You are welcome. Thanks for watching!

[@ahmedrashad7750]

You deserve likes and subscriptions

[@angelicanear3281]

Thank you! I love the step by step. This helps ME be able to teach others ❤!!

[@Johnson-l1r6x]

ong ong. slatt

[@antiscorbutic2091]

Wow thanks for the clarification,, my lecturer never mentioned anything about the 12 in finding the SD being a constant and I was so confused,,being that it was the same question I legitimately thought it was the 10+2 😂. Anyways thanks once again for the clarification 🙌

[@AceTutors1]

Thank you for the positive feedback! Yea, intro to stat courses often don't do a good job at explaining where certain things come from. If you are interested, here is a derivation of the uniform distribution standard deviation formula: www.quora.com/What-is-the-standard-deviation-of-a-uniform-distribution-How-is-this-formula-determined I'm glad we were able to help out!

[@bashmonaco4579]

What is that 12 in SD??

[@ShashankrajcI]

That was just great . your simple words explaination made me understand everything. please there is a request to make such content on poisoon distribution and hypergeometric and negative binomial

[@arsifali]

Great video! Short and useful

[@AceTutors1]

Thank you for your positive feedback!!

[@neyazahmed309]

You probably saved my semester

[@AceTutors1]

That is so amazing to hear! Thank you for your support!

[@ReenishMohanta]

Amazing Explanation !!

[@AceTutors1]

Thank you for watching and supporting!

[@dsjfnskjsdfbjdsbsksbfjk]

so easy and simple to follow, thank u

[@AceTutors1]

Thanks for the positive feedback! I appreciate you!

[@rishabhnarula1999]

thank you sir, really helpful, great teaching. 😊👍

[@mahmudulislam4705]

Thank you sir. It's been great help

[@AceTutors1]

You are very welcome! Thank you for watching!

[@massacreee3028]

actual life saver!

[@AceTutors1]

I'm so happy we were able to help! Thanks for watching!

[@mahmoudsa3eed696]

thanks alot i have final in 2 days and this saved me :)

[@mackenzyphilippe7508]

This was beautiful

[@AceTutors1]

Thank you for the positive feedback! I'm glad you thought so!

[@AprajitaSharma-p8u]

Great explanation .👏👏

[@lhosfoto]

THANK YOU ... NICE GRAPHICS ...

[@AceTutors1]

You are welcome! Thanks for the feedback and for watching!

[@HoomanOnEarth]

Whoa, thanks for making this video!

[@AceTutors1]

No problem! We are glad you found it helpful!

[@venzyking-jf2gv]

Binomial distribution thanks for the lesson

[@georgenader5340]

Wow 💯.. Thank you 💯💯

[@AceTutors1]

You're welcome! :)

[@cillarefinaldo5561]

Amazing Video!

[@AceTutors1]

Thanks so much for watching!

[@muhammadajmal562]

Thanks for great effort I appreciate it

[@AceTutors1]

You are very welcome! Your appreciation makes the effort worth it!

[@gauravmohan9271]

Thank you brother..so much..

[@AceTutors1]

You are very welcome! I'm glad you found in useful!

[@bernadettemburu6188]

My life saver❤

[@mushthakazhar8459]

great explanation thank u

[@Winnerdinner0]

i love the quote at the last

[@AceTutors1]

It's definitely something I believe and know some students can lose sight of when struggling with a class. Thanks for watching!

[@matthewfilgiano768]

This was great! Could you do a video on showing how the maximum entropy for discrete distribution is achieved by the uniform distribution in its general form?

[@AceTutors1]

Great idea! In short, the entropy of a discrete distribution is defined as "how much uncertainty" it has. If a certain outcome is 100% certain and the other outcomes have a probability of 0, then the entropy of the distribution is 0 because there is no uncertainty in what the outcome will be. On the other hand, the entropy is maximized when all probabilities for the outcomes within the distribution's interval are the same (AKA the uniform distribution). This resource does a good job explaining it: tdhopper.com/blog/entropy-of-a-discrete-probability-distribution but we will add this topic to our list of future videos!

[@dylanhall2993]

glad I'm not doing what you are doing holy shit.

[@wellness5736]

Thank You!!

[@AceTutors1]

You are welcome! :)

[@sanjanakhondaker887]

Thank you so much! :)

[@AceTutors1]

You are very welcome! :)

[@geetopriyoroy6537]

Please make a lecture series on various probability distributions with practical examples.

[@AceTutors1]

If you look through our channel you will see various videos on these topics.

[@juanproanoacosta9436]

Thanks a lot for these videos. Could you explain the gamma distribution as well?.

[@AceTutors1]

Thank you a lot of watching! :) Yes, that is something we plan on tackling in the future.

[@Farooq-s8v]

Amazing ❤❤

[@lizzaliz]

Thank you!

[@AceTutors1]

You're beyond welcome!

[@fhoooooooood]

Great stuff keep going 😁😁😁👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼

[@AceTutors1]

We really appreciate your kind words. It's the support of people like you that help us keep going!

[@Engineer78206]

great sir

[@learnunknownwithdave]

Thank you sir for the explanation,I have an exam on this topic on 07-02-2023

[@AceTutors1]

Nice! I'm glad we were able to help!

[@rakibhasan-nk1lv]

useful video with visualization

[@omarmarie7802]

Thanks ❤️

[@AceTutors1]

You are welcome! Thanks for watching! :)

[@aryanraj5558]

kindly upload all the videos in the playlist of statistics

[@AceTutors1]

We are working on putting out some new videos soon. Thanks for the comment!

[@MV-tm4re]

Thanks!

[@AceTutors1]

You are welcome! :)

[@HuyenNguyen-ed3uv]

thank you so much

[@JesseBrockwell]

your videos and animations look amazing... which software do you use?

[@EatSpicySweet]

Thanks much

[@AceTutors1]

You are welcome so much! Thanks for watching!

[@elizabethkain75]

So the area is literally just the space between whatever is less than X all the way to what is greater than X? And where did the 12 come from when you were finding the standard deviation? When finding the mu will you always divide by two? Or will you use a different number depending on the problem?

[@AceTutors1]

Hey Elizabeth, great questions! Yes, the area is the space under the curve between whichever x values you are trying to find the probability of. As for the standard deviation, the derivation of that formula is a little complex and outside the scope of this video. It comes from some statistics identities that are applied to the uniform distribution. As a result of performing those calculations, a 12 happens to come out. A great derivation and explanation of this standard deviation formula can be seen here: www.quora.com/What-is-the-standard-deviation-of-a-uniform-distribution-How-is-this-formula-determined As for the mean (mu), yes, you are always going to divide by 2. This is because the mean happens to be directly in the middle of curve due to its symmetry. So essentially you are finding the middle or average of the bounds a and b. To take the average of 2 numbers, you add them up and divide by two. Let me know if you have any additional questions!

[@lk6977]

@@AceTutors1 thank you! My college textbook gave us a formula and I had no idea how to use it and my professor didn't explain it well so I'm two weeks behind the class and have been binge watching anything off KZbin but this was the first video that made sense!!! Thank you so much! And thanks for the link!

[@AceTutors1]

@@lk6977 I love to hear that we were able to help you out! We have a bunch more Stat videos on similar topics so be sure to check those out too! We appreciate your message! :)

[@janpoonthong]

Great video

[@AshrafAlvi01622835512]

Please create one with a convex optimization problem and a solution to a primal/dual lagrangian problem.

[@AceTutors1]

Thanks for the great feedback! We will consider making videos for these topics in the future

[@oussamahajali2446]

thaaank you

[@AceTutors1]

Thank you for watching and passing on your kind words!

[@TheRickmint]

Thank you for your videos Clear and amazing to watch! Do you have time to create a video about multivariate normal distribution as well? Thanks

[@AceTutors1]

Thank you for your kind words! Yes, we plan on tackling topics like this in the future!

[@nicolechary5583]

Hi, thank you for sharing. Im confused on how you get the 10-2 at the end ? Thank you in advance

[@AceTutors1]

Great question! We got 10 and 2 from the problem statement that said arrives uniformly late between 2 and 10 minutes.

[@abdelruhmanessam8798]

Thx Sir 😊

[@AceTutors1]

You got it! Thanks for watching!

[@yacineg_dp600]

what kind of software you use to do these cool animations ? great video BTW, thanks XD

[@AceTutors1]

Thank you! We use Manim to generate the animations!

[@rahimmahmud697]

I have a question. In your exercise, we saw that you have to find the probability for being late . The person will be late when it is more than 7 minutes. But why did you take equal or greater than 7 ?

[@AceTutors1]

Great question! That is a very tricky concept, but it ultimately comes from the fact that the uniform distribution is a continuous distribution rather than a discrete distribution. Because it is continuous, the probability of x equaling any specific number is actually 0! For continuous distributions, we can actually only calculate probabilities across an interval of numbers like from 7-10 or 3-4 or something. With this information, we actually find out that the probability of being greater than 7 is the same and being greater than or equal to 7 because that additional probability of being equal to 7 is actually 0, so it doesn't add anything. I know this is a bit of a complex concept to wrap your head around, so if you have questions about this, please feel free to reach out!

[@fiazsila1187]

I like this 🎉

[@niluthonte45]

thank u yes helpfull.

[@AceTutors1]

Awesome! Thanks for watching!

[@Nimzi_world13]

Sir plz explain the Exponential Distributions

[@AceTutors1]

That is something we definitely plan on covering soon! Thanks!

[@filipzdravkovic7134]

Where did you get the 12 in the SD formula ?

[@dhvanipatel6449]

So good can you make for deterministic modelling and optimization please?

[@parthividrupad]

Thanks

[@syrknight1693]

Which app are you using to make the transition between slides very smooth? thanks in advance.

[@AceTutors1]

We are using software called Manim to make the animations. It's free and open-source too!

[@kennnat8507]

Make a video on normal distribution

[@AceTutors1]

We actually do have a video on this topic. You can find it here: kzbin.info/www/bejne/rnqci3t9hLiUeck&lc=UgzDaA0mYL22gzIo4VJ4AaABAg

[@VenujanSrithar]

can you please prove the S.D of uniform distribution ?

[@ashrafta4188]

I have a ❓ Is the significance test f, student test distribution Is the same like normal distribution I n another I want to compare between reeding of two analyzer instrument, automating tech I think their reading don't follow normal distribution

[@AceTutors1]

Great question! The F-distribution and normal distribution are similar in that they are used in hypothesis testing and confidence intervals, but they are used in different contexts. The F-dstribution is often used in ANOVA testing and to test if variances of two populations are equal.

[@dennisdwitama9206]

sir if the bus is uniformly late between 2 to 10 minutes, isn't that mean there are 9 sample space? which is 2,3,4,5,6,7,8,9,10 minutes? so why is the probability of the bus late >7 minutes is not 3/9 = 1/3 (3 because more than 7 minutes means 8,9,10 and 9 is just the total sample space)

[@AceTutors1]

Hi Dennis, great question! So the answer to this is the difference between discrete and continuous distributions. If it were a discrete distribution, you'd be right. The only outcomes would be all whole numbers between 2 and 10. However, this is actually a continuous distribution. This means the sample space is actually all the whole numbers you mentioned, as well as everything in between. It's infinite! The bus could arrive exactly 7 minutes late, but it could also arrive 7.5 minutes late, 7.25 minutes late, 7.00000001 minutes late and so on. So instead of taking the # of possibilities that satisfy what you're looking for and dividing by the total # of outcomes, as you would if this uniform distribution was discrete, you would actually take the width of the desired sample space (7 to 10) and divide by the total width (2 to 10). This results in the fraction 3/8 we found in the video. If you have any other questions, please feel free to ask!

[@dennisdwitama9206]

@@AceTutors1 Thank you! Very helpful and clear video explanation

[@AceTutors1]

@@dennisdwitama9206 Thank you Dennis for the support! I'm glad we were able to help!

[@গোলামমোস্তফা-শ৮থ]

Is it continuous distribution?

[@AceTutors1]

Yes it is! Great question!

[@russelmalit1761]

sir how did you solve the standard deviation?

[@AceTutors1]

Hi Russel! To solve for the standard deviation, you would use the formula discussed in this video, where b and a are the upper and lower limits of the distribution.

[@bobasuop]

best vid !!

[@user-ow7ps5gz2k]

Please, help me! How to calculate autocorrelation in uniform distribution?

[@AceTutors1]

Great question! And that is actually beyond my area of expertise, unfortunately. Perhaps a resource like this can be helpful: dlsun.github.io/probability/autocorrelation.html

[@pacificbhumihar6431]

Superb

[@AceTutors1]

Thank you very much!

[@1212bravo]

What does uniformly late means literally ? Can you explain please

[@AceTutors1]

That means that the time that the bus is late is uniformly distributed. This means that there is an equal chance (or probability) of the bus being late anywhere between 2 and 10 minutes. That means it has an equal chance of being 3 minutes late vs 5 minutes late vs 6.397 minutes late. This can visualized by the the probability distribution just being a straight horizontal line.

[@WilfredoOlankaOlonan]

Sir, can we apply this to lotterty? Or give some example about the probability topic on any distribution if any.

[@xoda345]

shouldn't the probability between C and D be the same as A and B? the height remains the same for the large rectangle as well the middle rectange( with C and D)

[@AceTutors1]

Great question! You are right that the probability distribution has the same height or value throughout the entire interval for a to b, but probability itself is actually the area under the curve. The area (AKA the probability) is different from a to b compared to c to d.

[@ariah5093]

How do I find the probability that it would be "Exactly 4"

[@AceTutors1]

Great question Ariah! In order to understand that, you need to know whether this is a discrete or continuous distribution. The uniform distribution is actually continuous! This is because the possible outcomes for the arrival of the bus is infinite between 2 and 10. The bus could arrive exactly 7 minutes late, but it could also arrive 7.5 minutes late, 7.25 minutes late, 7.00000001 minutes late and so on. Because there are an infinite number of outcomes, the probability of any one of those outcomes is always actually 0! That is why, for continuous distributions like this one, we will only ever really be asked to find the probability between 2 values like we did in this video. I hope this helps!

[@ariah5093]

@@AceTutors1 thank you! Well said, and exactly what I need!

[@adam62273]

How to find percentile from uniform distribution?

[@AceTutors1]

Great question! You can find the percentile of a given point within the distribution directly by finding the proportion your point is from the beginning (left side) of the distribution's interval with respect to the entire interval's width. For example, if its uniformly distributed from a=1 to b=5 and we want to find the percentile of some point c=2, we would divide (c-a)/(b-a) which would be (2-1)/(5-1) = 1/4 = 0.25 which means c would be the 25th percentile. I hope this helps! :)

[@Sammi1-ps2]

Isn't the formula for S.D= sqrt((a-b+1)²+1)/12)

[@simengwenya4310]

Thank you. Sketch the probability density functions and cumulative distribution functions of the following distributions, and in at least two of these three cases give examples of real-life situations where a random outcome is obeyed (possibly approximately) by these distributions: 1. Uniform(−1, 3). can you please help me solve this question.

[@antisocialbarbie1587]

Normal approximation please 😊

[@AceTutors1]

That's something we plan to cover soon! :)

[@pradeeppoi2735]

Sir can you plzz tell how to find a and b if P(X

[@AceTutors1]

To answer that question, we would need a bit more information. From that info, we know that the probability (or area) of being to the right of 1/3 is 0.5. Since this distribution is uniform, the fact that we have the area is 0.5 tells us that 1/3 must be exactly halfway between the endpoints a and b. However, we don't know exactly how spread out the distribution is. For example, if a = 0, then we could figure out that b must be 2/3 in order to satisfy the fact that 1/3 is directly in the middle. However, if a = 1/6, then this would imply that b is 3/6 (or 1/2) in order to satisfy 1/3 being in the middle. Without any additional information we wouldn't be able to say exactly what a and b are other than that they are equidistant from 1/3.

[@vanshikajain373]

Topic - continuous random variables

[@AceTutors1]

That's a topic we plan to cover soon! Thank you for your suggestion!

[@TaonasheMambizo]

How to find ex^2

[@paullin178]

How come mean is a+b/2. It must be. ( b-a)/2

[@AceTutors1]

Great question! So the mean is (a+b)/2 because you are essentially finding the midway point between a and b or the average of two number which is what the formula gives you. (b-a)/2 would give you half of the interval between a and b or the distance that the mean is from either endpoint, so you could take that value and add it to a or subtract it from b to get the mean.

[@mphff]

i dont see you x value has exact same y value between a to b

[@AceTutors1]

So the same y value existing for all x values between a and b can be seen by the flat line in between those points. At every x between a and b, the y value is the exact same, so when you plot it, the line looks horizontal; it does not go up or down at all.

[@ryancordano7209]

you saved my math grde how much to be my toutur

[@AceTutors1]

Hahah that's great. You can check out our website: theacetutors.com to see if we are at a university near you! ;)

[@abdulmateen0807]

May Allah bless you with Islam

[@redhairedshanksfanboy5695]

Explain it in One piece terms please.

[@UrjaKumari]

You didn't describe discrete uniform probability distribution and didn't even bother to describe how we got the formula for standard deviation.

[@AceTutors1]

Thanks for your comment! Yea, this video is just meant to be a high level overview of the continuous uniform distribution and its overall key formulas.

[@alexzheng982]

Something's up with your microphone, it is a bit quiet.

[@kaansenmanat7991]

Clean

[@malixx662]

thaks b

[@ianbowen4742]

beast

[@gottod6895]

Thank you.

[@akhildas4731]

❤❤❤❤

[@CHBSHUBHAMBAPUSHELKE]

❤️💞

[@AceTutors1]