Cumulative Distribution Function : Example : ExamSolutions

[rahul89dot]

so nice its was very helpful .................

[TheCornerKebab]

I understand that, kind of, but i have trouble transfering this to other questions. Do you have more? The one i'm doing now has an x on the first function too, so it's not working for this question what you're doing there.

[mrmaaza123]

Hey the video was good and really helpful, but i am having some problem in converting  pmf into cdf . How to we convert these discrete functions into cdf's? hope you can help me out with this .

[julieetran]

In terms of whether using less/greater than or equal to, or less/greater than, do you just following the original f(x)? Cause I'm having trouble understanding how to know which one you should use

[ExamSolutions]

@julieetran follow the original f(x)

[TheXAER0]

why is it that the llimit is x and 1? isnt it 1 and 2 because its also =?



[sonicheroin]

is the last answer must be 1??

[ExamSolutions]

@sonicheroin yes

[The1000ankit]

can you please explain why F(x)=1/4*x for 0<=x<1 instead of F(x)=1/4 ?

[vincentcold]

@The1000ankit You integrate 1/4 from 0 to x, so you would get 1/4(x-0) = 1/4x. the basic formula for CDF is integral of fx(t) dt over the range from - infinity to x where fx(t) is probability of density function. You can kindda say CDF is Fx(x) accumulates probability from the initial point up to a value x. CDF can be used to described both discrete and continuous random variables that's why it's convenient to use it.

[The1000ankit]

@vincentcold thanks it helps,,

[4216Mickster]

Again, well done! Concise and easy to follow. Cannot thank you enough.

[mysky1]

Thank you! It was very helpful! :)

[choiduck]

i don't understand the last part with F(X) = 1 when x>=2???? please explain

[ExamSolutions]

@choiduck Look at it like this, suppose you have a normal fair die. What are the cances of getting a number less than or equal to 7 say. Guaranteed so the probability is 1. F(X) = 1

[813queenPearl]

@ExamSolutions Thank you so much! Wasn't my question asked, but I definitely hunted all over Google for this exact explanation. Great video!!

[halovir]

ooooooh, so this is what my textbook's trying to tell me

[MissAyagoz]

Sorry, but its not clear for me why do we have to add that "extra bit" on? That area (1/4) does not belong to the interval [1;2]. It is between 0 and 1. Could you explain why do u add it?

[ExamSolutions]

@MissAyagoz Cumulative probability is the probability of being less than x which must include all area to the left of x which includes all the rectangle and part of the curve when x lise between 1 and 2

[mss3331]

I am arabic person but I understand the fu******king whole thing..

thanks alot ..plz keep going

[Morelloo1]

what happens if the intervals do not perfectly fit together.. eg. 1/4 when 0 <= x < 1 and x^3/5 when 2 <= x < 3? wat do you put when x takes a value between 1 and 2? is it just 0 ?( if assumed 0 otherwise). What I was thinking is that you would use the cumulative rule and take integral of 0 + 1/4 when 1 <= x < 2 but I am not sure if this is correct.

[andrum09]

You sound like Paul Bettany

[tjura1]

0.o Didn´t understand anything.. Maybe cause i´m norwegian..

[DizzyMartian]

Do you add the extra rectangle on because it's a cumulative function? :)

[ExamSolutions]

@DizzyMartian yes

[ribenaholic]

DUDE, u r the reason i'm gna pass!!!

[ExamSolutions]

@ribenaholic Hope you do. Let me know.

[chrisrock1990]

keep up the good work u and Khanacademy are really helping me make university a breeze.

Eternally Grateful. Maybe in the future i will help ppl out like you 2 do.

[ExamSolutions]

@chrisrock1990 Thank you for your support

[youartoyube]

Hey. This is great stuff. I'm a TA in statistics. I was just wandering if I'm allowed to put this link on my homepage so my students could see it?

cheers

[ExamSolutions]

@youartoyube Yes, that is fine.

[milescend]

This was really useful, thanks :)

[ExamSolutions]

@milescend Pleasure

[KostasA89]

your work is excellent!It helped me a lot!

[ExamSolutions]

@KostasA89 Thank you

[sajibratul]

hellooo can u guess plz hlp in thz one.....the discrete random variable has c.d.f F(x) defined b F(X)=2+x/7;x=1,2,3,4,5....find­ probablty distribution for X ..............ans is 3/7,1/7,1/7,1/7,1/7.....anyone can plzzzzzz explain it how...........

[sajibratul]

hellooo can u guess plz hlp in thz one.....the discrete random variable has c.d.f F(x) defined b F(X)=2+x/7;x=1,2,3,4,5....find probablty distribution for X ..............ans is 3/7,1/7,1/7,1/7,1/7.....anyone can plzzzzzz explain it how....

[Managirl112]

I probably would have missed it out too! Thanks!

[Bugatti360]

good stuff

thanks man

[ExamSolutions]

@Bugatti360 Thanks mate

[mauroprovatos]

what if X is discrete?

how do you find the cumulative distr. function then?

[ExamSolutions]

@mauroprovatos If it is dicrete the probabilities are given in a table. Just add each probability up. So if P(X=0) = 0.1, P(X=1) = 0.3, P(X=2) = 0.6 then the cuymulative distribution function F(X) is given by F(X=0) = 0.1, F(X=1) = 0.1 + 0.3 = 0.4, F(X=2) = 0.1 + 0.3 +0.6 = 1. Hope that helps?

[mauroprovatos]

@ExamSolutions yeap, it sure does.

Thank you very much.

[mauroprovatos]

@ExamSolutions but what if the discr. variable values are given through a function?

Can you derive the cumulative?

Because the values of X are countably infinite

[Raghunandan419]

thanku



[ExamSolutions]

@Raghunandan419 Nice to hear that it helped - thanks.

[Mifune00]

Thanks!! It was very helpful.

[marxyification]

Thanks a million for the video, great explanation, u just saved me.

[ExamSolutions]

@marxyification Cool!

[maccadiodrums]

So basically, you always use the lower bound on the next new range past the previous function? I think that would be the universal interpretation of this aid correct?

[Desalicious90]

you are awesome!!! awesome explanation, voice and handwriting lol. THANK YOU

[ExamSolutions]

@Desalicious90 Steady on but thanks.

[th2]

Another great video

[ExamSolutions]

@th2 Thank you for your continued praise

[Rand0mAsian]

i just want to say thank you very much, this was very helpful! i was kinda stuck on why the upper limit you used x, but i read the comments and understood. thank you again.

[boyd1876]

Love the video, very helpful unlike my droning college professor. However, at around the 8 minute mark when you are defining the CDF, shouldn't it be for x is less than zero = 0 as opposed to x is less than or equal to?

[ExamSolutions]

I know what you mean and this is always a point for debate.

[chawin30]

@boyd1876 that what I was thinking also

[3ej6]

I went to this video to help me answer this exact same question was stuck on!! Thanks you very much!!

[lovescs]

when finding x more or equal then 1 and less or equal than 2 why have to include the rectangle?? i thought it only include the curve area??

[ExamSolutions]

Cumulative probability is the probability of being less than x which must include all area to the left of x which includes all the rectangle and part of the curve when x lise between 1 and 2

[ExamSolutions]

Always integrate from the lower limit to x so that you get the area to the left of x in otherwords the probability of being less than x.

[ExamSolutions]

because this would give you the probability of being less than 2 which would equal 1 and secondly you need to the probability of being less than any general value x.

Hope that helps?

[hatimali04]

I love your approach and that accent ;)

This has seriously helped me gain some confidence in my probability class

[ExamSolutions]

Thanks