How to find a cumulative distribution function from a probability density function, examples where there is only one function for the pdf and where there is more than one function of the pdf.
I'm trying to brush up on my stats for a course on Bayesian Machine Learning, and this is the clearest example I found. I thought this is how the cumulative distribution function worked, but the other sources I encountered were less approachable for someone who hasn't taken stats in awhile. This used basic integral calculus and confirmed that my intuition was correct. Thanks!
@@hk254lyt8 Hey. It's good! I have been working as a data scientist for a year and a half, and have a modeling pipeline I built for personal projects.
I'd also like to thank you for very effective teaching in this video! It's great! Just one minor thing that I nevertheless think could increase its quality is if the writing could have been less hard to interpret :) It's a bit like Doctors handwriting ;). I know, there may be technical aspects at play, but still, it's just my well-meaning suggestion.
greaaat explanation i finally could understand the concept thanks to ur video, please just consider improving the way u write, other than that, just continue adding some of these awesomeee videos. danke schÖn
Awesome video my man! Just a quick question, at 5:00 why do you put 1, x>3 instead of 0, x>3? Doesn't it say 0 for all other values outside of the range of f(x)?
A CDF is the cumulative probability. So, the sum of the probabilities up to that point: P(X>3)=1. The graphs of the pdf and cdf are different. He did not graph the latter.
Yes, but this now a is a cumulative function, which is different to the probability density function. It means that the area under the curve will be 1 for any point where x>3, because we are counting all of the area up to that point.
for the f(x) then , then yes x>3 is 0. but since its F(x) which is the CUMULATIVE distribution function, the value is for x>3 is 1 since the total area for overall is 1. the total area is 1 when the range is between 1-3. anything above 3, is considered more than 1.
I have a question (in the 1st problem). I understand why the cdf becomes 0 when x < 1. But... The cdf is (x^2 - 1)/8 if 1 ≤ x < 3; and the cdf is 1 if x ≥ 3, aren't they?
I think you’re referring to the inequality signs relating to 3. When x is 3, F(x) = 1 either way. Whether you say F(x) = 1 when x ≥ 3 or F(x) = (x^2 - 1)/8 when 1≤ x ≤ 3. Substitute 3 into this and you still get 1. So doesn’t matter whether you include 3 in the second or last statement. This is because the probability of an exact number = 0. So the inclusive inequality signs are pretty much irrelevant.
It's because we are looking at a cumulative function. The limits of the pdf is between 1 and 3, so anything before 1 the probability is 0. Anything above 3 the probability is 1, because the cumulative function encompasses everything up to the number inputted, if you choose a number 3 or greater, it will have given the area of the entire function, which is 1. Hope that helps.
I'm trying to brush up on my stats for a course on Bayesian Machine Learning, and this is the clearest example I found. I thought this is how the cumulative distribution function worked, but the other sources I encountered were less approachable for someone who hasn't taken stats in awhile. This used basic integral calculus and confirmed that my intuition was correct. Thanks!
Hey from the future 👋. How is your machine learning journey so far? 😅
@@hk254lyt8 Hey. It's good! I have been working as a data scientist for a year and a half, and have a modeling pipeline I built for personal projects.
Can't tell you how much I needed this. Many thanks from myself and my grade!
This was so simple, concise and clear to understand! Thank you!!
Crisp, clear and very concise. Thanks mate!
5 years later still helps me greatly thank you!!!
Can't tell you how much this one has assisted me, thank you
I really have to watch this like more than 10 times because of the graph, it’s not clear 🙁. But this was all the eplanation I needed. Thank you.
Thank you. This was a super, super clear explanation.
Thank you, bless you Sir. no time wasted straight knowledge straight facts, you're a beast.
Thank you for explaining through these easy examples .
you're THE MAN, thanks so much, got theory of information exam in less than two days, you saved me
Great job explaining. Very clear and to the point. Thank you. The way you write the x tho really bothers me hahah
Thank you for your clear explanation. It's super helpful!
Thank you so much, you really saved my life on understanding the concept!
I'd also like to thank you for very effective teaching in this video! It's great!
Just one minor thing that I nevertheless think could increase its quality is if the writing could have been less hard to interpret :) It's a bit like Doctors handwriting ;). I know, there may be technical aspects at play, but still, it's just my well-meaning suggestion.
Thanks!! Keep posting more...I will tell my friends of your channel
Help me please, is there any difference between corresponding distribution function and cumulative distribution function?
Thanks mate.Keep up.You're the man.
Thanks very much.
It saved the day.
Sarcastic part was 8:20, the background looked like a truck was coming.
Many many thanks to you bro .. I need the most... honestly
is it okay if we dont subtitute values and just get the function
for example without substituting the value in second part function we get is 7+2x3/21
You're incredible! Thanks you so much!
good explanation sir.u have done a great job.
Really helpful, thanks!
Awesome Vid! Much appreciated!
Really helpful, thank you a lot!
Finally I found the best explanation video❤
The variable under integration should be something different from x, say 1/4tdt. Very well explained
Great!!!!! Thank you so much for this
That was the first question of the midterm of the Modeling and Discrete Simulation course at Marmara University.
Very nice! It really helped me.
Thanks, helped me a ton.
Incredibly, thank you so much!!
greaaat explanation i finally could understand the concept thanks to ur video, please just consider improving the way u write, other than that, just continue adding some of these awesomeee videos. danke schÖn
Why does x stay the same instead of being multiplied with the xˆ2 inside the bracket and hence becoming xˆ3? Pleaseee anyone answerrrr
Thankyou !!!!! It is very helpful
Sir, when you are using "x" as a limit how can you integrate the PDF using "dx". Shouldn't you use a dummy variable?
X is a variable value between 1to3 for finding the probality at any point
Yes. Bad form not to.
Could you please explain why you have X^2 / 2? Is f(x) by definition x^2?
why in 1st example the probability is 1 after 3 ..Reason ?? the graph is still touching zero as in case of x less than 1
if question is P(X+Y>3)..........what should i do?
Great video. Thanks :)
great video, thank you!
well explained.Thankyou
Why do you get a probability that is greater than 1? For instance with the second example f(x)= 2/7*(2^2) >1 ... surely it doesn't work?
Thnx for explaining...ND no problem with handwriting, Its better than mine
Good work, my g.
awesome video bro thank yu verymuch
You are totally amazing
You are awesome man
Great Explanation😌
perfect..never found something simpler!
great explanation
Awesome video my man! Just a quick question, at 5:00 why do you put 1, x>3 instead of 0, x>3? Doesn't it say 0 for all other values outside of the range of f(x)?
A CDF is the cumulative probability. So, the sum of the probabilities up to that point: P(X>3)=1. The graphs of the pdf and cdf are different. He did not graph the latter.
Yes, but this now a is a cumulative function, which is different to the probability density function. It means that the area under the curve will be 1 for any point where x>3, because we are counting all of the area up to that point.
thank you for this.
you saved my life ...
Well explained 🙏
very helpful, thank you
bohat papi samjhaya re, love from Pakistan
why would you add area of A i. e. 1/3*1...??? There is an integration that will add the area already..
wonderful thank you man
I understood everything, thank you! In part 2, F(x) is x/3 when 0
Because its continuous, it doesn't really make a difference because the probability of x=1 is 0
Excellent!
Thank you so much
Really nice 👍
Better than my lecture can I pay you the tuition instead
Thanks man :)
Thank you!
Your voice sounds nice.
why is it 1 for x>3? shouldn't it be 0?
for the f(x) then , then yes x>3 is 0. but since its F(x) which is the CUMULATIVE distribution function, the value is for x>3 is 1 since the total area for overall is 1. the total area is 1 when the range is between 1-3. anything above 3, is considered more than 1.
Error in the final F(x)
In the cdf while writing the function for 1
Ok, I see what is happening... duh! As the name suggests it is cumulative. Similarly p(x)=0 for x>2 but P(x)=1 for x>2! Got it. Thanks.
I have a question (in the 1st problem).
I understand why the cdf becomes 0 when x < 1. But...
The cdf is (x^2 - 1)/8 if 1 ≤ x < 3; and the cdf is 1 if x ≥ 3, aren't they?
I think you’re referring to the inequality signs relating to 3. When x is 3, F(x) = 1 either way. Whether you say F(x) = 1 when x ≥ 3 or F(x) = (x^2 - 1)/8 when 1≤ x ≤ 3. Substitute 3 into this and you still get 1. So doesn’t matter whether you include 3 in the second or last statement.
This is because the probability of an exact number = 0. So the inclusive inequality signs are pretty much irrelevant.
thanks chief
welldone man
thanks man
How we get 7??
I love you thank you
thank you!!
Hate to be nitpicky, but why do you draw your x's like that...
Thanks sir.
Thank you :)
Thanks a lot
the second part answer should have been
7x+2x3 /21
no?
Thanx sir
Thanks :)
thank you.
Brilliant
thank you bruv
Keep it up
the video gives useful information, thank you very much
better handwriting next time XD
why is the probability 1 at x > 3
It's because we are looking at a cumulative function. The limits of the pdf is between 1 and 3, so anything before 1 the probability is 0. Anything above 3 the probability is 1, because the cumulative function encompasses everything up to the number inputted, if you choose a number 3 or greater, it will have given the area of the entire function, which is 1.
Hope that helps.
ty :D
tnx sir
how to find cdf from pmf
thankyou
thats wassup dawg on god
you sound like you could be a harry potter character
hye sir
convenient
Sorry i didn't understand the drawing. :(
I didn't understand anything 😭😭😭
this is unclear put the camera closer to the paper next time I cannot see anything