Finding Probabilities and Percentiles for a Continuous Probability Distribution

[@asols4318]

You are incredibly clear and thorough with your teachings. Can't tell you how much I appreciate it. Keep it up!

[@pedrofernandes4050]

I have no problem understanding statistics but the time it takes. Some tutorials want to be so precise its complicated to get it at first, others are so basic and easy that leave important content out. This dude just gets it right, thanks.

[@michaeljagdharry]

These are extremely clear. I am studying to be an actuary, and this is the clearest learning resource I've used.

[@jbstatistics]

Thanks very much Michael. I'm very glad you find my videos helpful.

[@daniyaryeralin9813]

I watched about 4-5 videos on KZbin (approximately 15-25 min long), but I couldn't understand anything from what they said. I watched this 12 minutes video, and I feel like I'm master of Continuous Variables :D Thank you!

[@jbstatistics]

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

[@EmmanuelChegeni]

These videos are way better than my lecturer, nice job!

[@jbstatistics]

Thanks!

[@chaitanyadangeti5607]

True

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@@jbstatistics Can you please do a video on Weilbull Distribution and Weilbull Fitting? Thanks

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Watching these videos actually make me want to learn and be interested in statistics!

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After starting taking your stats course, most of the things I had a hard time trying to understand before, started making sense. And having the opportunity of reviewing topics from the class by watching your videos is great! Thanks for taking the time to do that!

[@jbstatistics]

I'm very glad to be of help Aline!

[@flamingoKnight]

Great explanations, terribly underrated channel. I hope you get the attention you deserve!

[@jbstatistics]

Thanks for the kind words!

[@AlienBlade51]

can't praise this dude enough!, you have no idea how much you are helping me on my Mathematical Statistics course! can you make a video about the Gamma distribution please?

[@LoganLovell]

thanks for saving my grade. crazy how a 6 year old video helps me understand things better than an in class lecture....

[@jbstatistics]

I'm glad to be of help. The calculus didn't change in the past 6 years :)

[@Aqeelaqeelzeid]

Best Explanation on statistics on the planet ! All stat students must watch these videos !

[@satu272]

These videos are great. Not often do you see something super clear and concise at once, so thank you for making them! PS. The way you draw an x is quite unique, at first I thought it was some mathematical symbol I didn't know about :)

[@julieye5832]

Wow! Yet another clear and no nonsense video!!! Thanks!

[@Kasun_Ish]

You're explaining the concept at point.This was very helpful to understand concepts.Thanks.

[@sarygirl4776]

omg. you just saved me from failing my exam! Thank you so much.

[@jbstatistics]

+SaryGirl I'm glad I could help. Best of luck on your exam!

[@keshavkumar7769]

HATS OFF TO U MAN . U R JUST INCREDIBLE . I HAVE SEEN MANY VIDEOS , BUT MY CONCEPT IS NOT CLEAR . BUT AFTER WATCHING YOUR VIDEO , WHAT I SAY IT JUST WAOOO.

[@lilmoesk899]

Your videos are awesome. Thanks so much for your work. I have one request! Could you make a video that explains the basics of calculus for probability? I haven't taken calculus since high school and I've forgotten most of it. But it also seems like overkill to have to relearn 1-2 semesters of calculus just for use in probability. Something like a "Basics of derivatives and integrals for probability" would be super helpful for someone like myself! Perhaps a few step by step examples of common use cases would be useful for others who either haven't done any calculus in a long time or just want a quick understanding of the computations and notation.

[@jbstatistics]

Thanks for the compliment and feedback. When I get back to video production I'll consider your suggestion. All the best.

[@jbstatistics]

Thanks Simon! I'm glad to be of help.

[@salonimittal6903]

Thank you for your great videos. Something is unclear to me. At 9:58, you said "F(x) is going to equal 1 when x is greater than 4", why does this happen even if random variable X can't take on values greater than 4? Please explain !

[@timsmith66]

+Saloni Mittal F(x) is the cumulative distribution function which takes on values between 0 and 1. f(x) takes on values between 2 and 4. F(x) is the sum of the probabilities that f(x) will be less than or equal to some number x. So, when you figure out F(5) for example, it is the probability that f(x) will be less than or equal to 5. Because f(x) is always between 2 and 4, it is always less than 5, and F(x)=1. When looking at the graph of the curve for f(x), to find F(x) you integrate to find the area under the curve. Again for F(5), you would find the area under the curve to the left of 5. And since the area under the curve from 2 to 4 is the only place there is area under the curve, and is equal to 1, anything higher than 4 will result in an area of 1, and thus F(x)=1.

[@D34tho]

+Tim Smith I guess I get it from the word "cumulative" we're taking infinitesimally small values until we reach x, if we're taking 5 we're going to go from 2 "collecting" then reach 4 having collected 1 then ending up continuing collecting zeros from 4+

[@amantekle127]

I have watched a few of your videos and found them really helpful. Thank you for sharing!

[@MP-py7ji]

Great! All your videos are awesome. Excellent teacher and beautiful graphics.

[@HelloYouThisIsMe]

you're a baller. Very clear and concise.

[@jbstatistics]

+HelloYouThisIsMe Thanks!

[@Cleisthenes2]

Is this the main reason you need calculus for stats? Because then you can measure the area under a curved line on the graph?

[@jbstatistics]

That's one (important) reason, but there others, such as finding maxima and minima.

[@jbstatistics]

You are welcome. Best of luck on your test!

[@claireoneill3955]

This is currently saving my stats 425 grade intro to probability is not easy but these videos make it easier

[@NChatterjee]

Thank you sir for teaching so clearly.

[@rogelaycardo2457]

Amazing discussion. Very clear and precise.

[@DannyLaam]

OMG thank you so much for being better than my f-cking school book.

[@MrAdelromio]

u have a great voice ,,, u should to work on Radio ;) or to do some Documentary ;)

[@jbstatistics]

Thanks! If I ever lose my job I might have to try that!

[@andrewagita901]

@@jbstatistics asmr

[@simontadesse5356]

You are just awesome! Clear and effective lecture.

[@MrSherzad13]

Great video, thank you very much! I did not quite get one point, when we have figured out F(x) and let's say x=5, will F(x) be equal to 1. Why not 0 because it is outside of [2, 4] range?

[@jbstatistics]

F(x) = P(X

[@joshua.guevara]

jbstatistics Is it possible you could just slightly elaborate on this? I'm a little confused still. " Since P(2

[@timsmith66]

+Caribbean Josh F(x) is the cumulative distribution function. That is, the total of all the probabilities (cumulative) up to that point. The reason being, if you want the probability that the result is less than 3, you add all of the probabilities for the values to the left of 3 (or in this case, integrate to find the area under the curve to the left of X=3). Therefore, because all of the values are between 2 and 4, the probability of the result being between 2 and 4 is 1 (or 100%) and also, the probability of the result being less than any number higher than 4, is also 100%. All of the results are less than 5, 6, 7, etc. (there is a 100% probability that the result will be less than 5, 6, 7, etc.)

[@jbstatistics]

You are very welcome!

[@elyorbekibrokhimov6754]

You are wonderful, I learned a lot from your videos

[@jbstatistics]

I'm glad to be of help!

[@777ISR]

Amazingly easy to follow. Thank you.

[@jbstatistics]

You are very welcome!

[@fardinahsan4319]

10:07, how is F(x)=1 if x is greater than 4? (Since x is ranged from 2 to 4)

[@zarahabubakar7986]

I’m so glad I came across this video I now understand so well But please I have a question that I was not able to solve Is there anyway I can send it to you for help? Thank you.

[@johamad5148]

In 8:39 why is the integral from 2 till x? why isn't it from 2 till 4? isn't the interval x between 2 and 4?

[@jbstatistics]

We're finding the cumulative distribution function F(x) = P(X

[@Jordan5293]

Your videos are awesome by the way, when you found the median on 7:44 isnt that the expected value also. Could we have used the same formula for expectation to find the same 'm'.

[@jbstatistics]

Thanks for the compliment. No, the median and expected value are not the same thing. If the distribution is symmetric, the mean and median are equal, but they are not equal in general. If we were to calculate the expected value of the distribution shown at 7:44, we'd see the expected value is 992/300, which is approximately 3.306667. That differs a little bit from the median that I calculated in this video.

[@ahidk7945]

how f(x)=1 when x greater than 4 at 10:04. It must be 1 when x between 2 and 4 not when x greater than 4 can u explane?

[@noahlove1955]

Ahid K He’s talking about the cumulative distribution function. This function asks what is the probability that P(X=x) is less than that number. Because everything is below 4 (and higher) you know it is 100% Ask yourself what is the probability that X is less than 5.6. The answer is obviously one, because X can only exist between two and four. Therefore, for any value greater than four, the cumulative distribution function equals one

[@lilyT_M_]

For integral bounds, does it matter if it is less than or equal to or strictly less than?

[@Didier-cu6cb]

The statistics and probability professor of our university taught us continuous probability distribution while we still don't know Integral calculus! Is it not possible to learn continuous probability distribution without integral?

[@jbstatistics]

I think it's fine to teach continuous probability distributions without explicitly discussing integration. e.g. Using vague statements like "Probabilities are areas under curves, and we can find those areas with mathematical techniques, and software has incorporated those mathematical techniques for us." I think someone can develop a very good understanding of statistics from that perspective. Keep in mind that most of the continuous distributions we use in statistical inference (e.g. normal, t, F, chi-square) do not have closed-form cumulative distribution functions and must be integrated numerically. So whether someone knows integral calculus or not, in the end areas are found using software. For a full and deeper understanding of what's going on? Sure, knowledge of integral calculus is meaningful. At a level to achieve an understanding of applied statistics? I don't think knowledge of integral calculus is necessary.

[@Didier-cu6cb]

@@jbstatistics Thanks for the quick reply🙏 I'm actually preparing for an exam, and when I got to the topic of continuous probability distribution, I got a little confused because of the integral. I meant more to solve exam questions related to continuous probability distribution than to have a theoretical understanding. It seems that to reach the final answer, you need to know integral calculus (or have an advanced calculator).

[@jbstatistics]

@@Didier-cu6cb For any of those distributions I named, and many others, there is no closed form solution for the integral. It does not matter how great of an integrator one is, the integrals can solved only by numerical techniques. We do that using software. The world's greatest integrator and a person knowing no calculus whatsoever solve the problem in the same way: By asking software for the appropriate area.

[@Didier-cu6cb]

@@jbstatistics Right. Thank you for your response & content.

[@Didier-cu6cb]

​Thanks to your contents, I got A grade in the statistics and probability course. Thank you so much​@@jbstatistics

[@veronicanoordzee6440]

I don't see what the difference is in definition between PROBABILITY and PROBABILITY DENSITY? How do you collect probability densities and make a curve/function of it?

[@jbstatistics]

Probabilities are represented by areas under the curve. The probability density can be thought of in a number of ways, one of them being that it's the rate of change of the cumulative probability at that point. In other words, the rate of change of the area as we move from left to right. We don't "collect probability densities"; a probability density function is a theoretical notion. There are a number of common probability density functions that, at least to a reasonable approximation, commonly occur in practice (e.g. the normal distribution, exponential, continuous uniform, t, chi-square).

[@veronicanoordzee6440]

Thank you very much! I work on it ;-)

[@justinlee417]

you the man jbstat. thank you.

[@jianxiongji2578]

please forgive me if i forget to click the "LIKE" button for all the videos I have watched in your channel. I have been trying very hard to make sure I clicked it for every single one of them.

[@SneakClub]

By any chance would it be possible to find the percentile when dealing with cdf?

[@TheAdlcn]

very very very helpfulll!!!!! really great video !!!

[@gila96aquila]

at 3:06 the plot of the pdf has the maximum value at 1, but I think it should be less than 1, otherwise the integral is more than one . However I won't pass the exam without you, Thank you

[@jbstatistics]

The maximum height of a pdf can be greater than 1, and is in this case. For it to be a (proper) continuous probability distribution, the pdf must integrate to 1, and this one does. Let's look at a simple example to illustrate. Suppose X has a uniform distribution on the interval [0,0.1]. Then f(x) = 10 for 0

[@RobertoEmilioRomero]

in the cdf example shouldn't it be true for values less Than 4 not greater than 4 as you noted x>4

[@jbstatistics]

The cumulative distribution function F(x) gives us P(X 4, which is true since P(X 4. (The random variable X must take on a value less than x if x > 4.) For values of x less than 4, F(x) is less than 1.

[@RobertoEmilioRomero]

I understand, thank you so much.

[@RobertoEmilioRomero]

When. X>4 F is 0.?😉

[@michaellarrauri9145]

Very helpful! Thank you sir!

[@mustafaawadelseed1962]

thank you very much , can you do two random variables X and Y

[@mahmoudakram6579]

this video is very easy to learn ability

[@marcoventura9451]

Very good video. I can't grasp why F(x) should be 1 even when x is greater than 4.

[@bajen118]

How did you get 240 in the denominator?

[@actionjessie]

Thank you I have a test on this on Monday. Dont follow in the lectures

[@alexhuseyni5795]

Great video!

[@sourabhjadhav7929]

Thank You very much.

[@andrewdeuriarte9147]

thanks for making this

[@owamsisanda527]

thank you very much Sir

[@vansikasingh3228]

Thank you so much!

[@ruirui_130]

Thank you so much

[@setripper]

I like your voice.

[@jbstatistics]

60 x 4 = 240.

[@pryoungster]

Great Vid!

[@jbstatistics]

Thanks!

[@alaaalkeswani2693]

Thank you sir

[@ashrafal-warraquiy6614]

Great Thanks

[@sethmariano9704]

Great!

[@jbstatistics]

+Seth Mariano Thanks!

[@lambsauces]

Legend

[@sarahhope8516]

Thank youuu :-)

[@jbstatistics]

You are very welcome!

[@jimjimmm]

Wheres percentiles ?????

[@jbstatistics]

I find the median, which is the 50th percentile. Use the same procedure to find other percentiles, setting the integral to whatever the appropriate value is in your situation (I set it to 1/2 in the video, as I was finding the 50th percentile).

[@jimjimmm]

@@jbstatistics alrightt thanks bruh

[@trobe23z]

Thank you. I am studying for the actuary exam and the way they explain these problems is an abomination.

[@jbstatistics]

I'm glad to be of help!

[@romeosantos8848]

you cannot just give a value to "m" its illegal