What is a Probability Density Function (pdf)? ('by far the best and easy to understand explanation')

Explains the probability density function (p.d.f.) and the mathematical notation that is commonly used.

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[Nothing-joci]

This video is the proof that nature isn't extremely hard to understand. Some people are just better at teaching than others. Thank you very much! I'm excited to watch as much videos as I can from your channel.

[vidakgrujic]

I need to thank you, 4 years of high school + 4 years of university could not explain me in this intuitive way. I have finally understood not only PDF, I understood the idea behind integrals too. Thank you so much, I feel blessed at the moment.

[calender]

It’s crazy how much better I understand once you gave the important fundamentals and graphs. I always wonder why professors skip this

[chillyvanilly]

I have to say, that your explanations Sir have just blown me away!
I very much appreciate this piece of knowledge that you Sir have shared with the world (especially Uni students)
in such an intuitive way, especially the integral-part!!
Thank you!

[neerajr]

Simply the best explaination I've ever got on the topic. Please keep up the good work and you will be helping a lot of engineers and other people out in the world.

[Carlosbl]

With a simple explanation the concept looks way more simple than before. Thanks Iain

[on_my_own_two_feet]

What makes this the best explanation of probability density function on YouTube is that you start with a concrete example of practical values generated by a random variable X (i.e. the time that it will take to get from A to B) and at the end, you bring it back to this same example; which makes it much easier to picture and to understand!
For the longest time, I couldn't even grasp the concept of 'density' in this context. Now that I've watched your explanation, I understand that the peak of the normal distribution corresponds to the most frequent probabilities in a data set, i.e. in case of normal distribution, most frequent/likely observations will have the probability roughly equal to the mean of the distribution (I hope I expressed this correctly).
Thank you so much for this video, Iian! You are a truly gifted educator. <3

[Collingwoodzone]

this is the first time i have properly understood the pdf, the equation and why the integral applies here. excellent explanation - subscribed.

[ella]

I literally wasted my 1 hour on searching this topic. You saved my time. You explained it so well. Thank you, thank you so much!

[gayathrigirishnair]

Thanks a lot for this simple yet impactful explanation. Probability represented in terms of calculus has always been a roadblock for me. Thanks for helping me in my journey on overcoming this.

[balinttothg]

a 2nd-year physics student trying to understand quantum mechanics is very grateful to you!!!

[LightHolmes]

My professors didn't even bother explaining the notations, added to the confusion about what they were trying to do. Thank you so much!

[anjangorai]

this particular video was more accurate and had a better explanation than the one on the khan academy channel. Thanks a lot for making this concept so simple.

[jsridhar]

This is by far the best and easy to understand explanation of PDF. Kudos to the author.

[rajatguleria]

Sir, you really ignited a spark in my mind regarding the need of pdf, I was struggling for long time.

[DeadMyth]

YOU ARE THE FUCKING BEST, idk why the fuck i pay tens of thousands to my university when the tutors just simply read out from the powerpoints word by word and skipping all the steps in between without explaining the logic

[ALI_B]

I appreciate your approach. It would make many students like the subject instead of disliking it.

[lg]

Must admit this was the best explanation of pdf ive ever heard

[bob-pqef]

wow this really made it click in my head, you are an amazing teacher!
Have you perhaps thought of doing a series on matrices, I would not be surprised if you know everything there is to know on this as well?

[yashs]

Amazing explanation, thank you so much! Could never understand prior what f(x) represented, but this video clarified all my doubts.