Conditional Probability given Joint PDF

After making this video, a lot of students were asking that I post one to find something like:
Pr(X greater than 1 GIVEN Y greater than 1)
... Please check out the following video to get help on this type of problem: • Conditional Probabilit...

[@Evil_Narwhal]

I really hate how the professors go over the simplest examples but then the homework has in depth problems like these. Thank you so much.

[@leahwilliams3281]

Seriously. Thank you. My professor didn't explain this very well, but it was totally on the homework. You did a great job explaining.

[@mclovinyousaucin]

you literally are the reason i’m gonna pass this module, not a single other video on the internet did it like you, exactly the terms and definitions i needed. GOD BLESS YOU ❤️❤️❤️

[@Stats4Everyone]

So happy to hear that you found this content to be helpful! :-D

[@wanhope3660]

explained in simple terms. helped me more than hours of listening in my probability class. Thank you !

[@kushalmohnot3808]

I've fallen in love; what an incredibly clear thought process!

[@Stats4Everyone]

Awesome! Happy to hear that this video was helpful :-)

[@StatsWithJesse]

Great video - thank you. I studied applied mathematics a few years back, and I quickly forgot some important things. I needed this video- it was clear and concise.

[@movocode]

Thank you sooo much - you helped me in very last moment of my exam prep - literally seeing this 1 hr before my exam starts. Love from India.

[@Stats4Everyone]

You're very welcome! I'm so happy that this video was helpful :-)

[@kkikkodan]

thanks so much. my sir did this in short but didn't give reasons for the way things were. so this was very helpful. love from India.

[@baqerghezi1342]

Great video thank you. also we can see the answer is 1 from the support (1

[@Stats4Everyone]

Yup. I am just showing the math for that logic. Here is another video where the answer is maybe not so obvious: kzbin.info/www/bejne/eHOzhICClMSbhdE

[@cleo7663]

Thank you for saving my life. Seriously.

[@mirandaatangdithebe3893]

Could'nt have asked for a clearer video, thank you sm.

[@Stats4Everyone]

Happy this video helped!

[@ahmetkarakartal9563]

you saved my life

[@darcash1738]

I see. so marginal is just integral in respect to the other var, with bounds according to that var. Then for conditional f|y it is f(x, y)/fy, where fy is the marginal prob. Then you plug in whatever the y val is, and do the integral in terms of x, with bounds updated to whatever the y val is.

[@pppeterrrr4776]

thanks, its very straightforward and clear

[@rye-bread5236]

Jesus. I regret college. I could have been a fantastic electrician and probably make almost as much.

[@topstuffspotter7878]

Great Explanation! and your voice is really sweet.

[@Stats4Everyone]

Lol. Shucks. Thanks :)

[@izume2032]

You saved me 😭💙 thank you so much

[@ghitrifaldiadrian4324]

your’re the best

[@Stats4Everyone]

Thanks for the comment, glad you found this content to be helpful :)

[@ghitrifaldiadrian4324]

@@Stats4Everyone yes, it really is, i’m currently struggling a bit on this topic for my mid semester. Then i found your video and all was crystal clear

[@mohitgupta3115]

thank u so much , i wish my professor learn how to tech like you

[@Stats4Everyone]

Glad you found this video to be helpful :-)

[@ihsanerben]

YA SEN NE BÜYÜK Bİ ADAMSIN BE KARDŞEİM

[@malcolmlamya8770]

Thank you, it helps a lot. God bless.

[@Stats4Everyone]

So happy to hear that this video was helpful!

[@YokiWong]

Thank you so much for the great video!

[@arnabbanerjee5833]

Thank you so so much for uploading this vedio... It helped me a lot.!

[@ARCWIZARD]

Thx ❤

[@chanakaramanayake8409]

Thanks a lot. Good explanation. keep it up👍

[@ruanvieira2545]

Great explanation, thanks!

[@lynejomaa7365]

tysm i have my stat final in 4 hours and might pass it thanks to this vid

[@Flowerlifts111]

did u pass

[@lynejomaa7365]

yes i did!!!! :D

[@vishwajiththippeswamy5714]

Thank you so much. Examples were very helpful :)

[@Stats4Everyone]

Glad it was helpful! :-)

[@ottodvalishvili7601]

great explanation .

[@bilgegursoy2599]

you are my savior

[@ericliu7705]

Thank you, this was very helpful

[@tvvt005]

5:21 wait but isn’t Y still between 0 and x?

[@kasunpathirana9410]

So understandable

[@quantowen1124]

Love it!! Could you please create playlists.

[@Stats4Everyone]

kzbin.info/aero/PLJDUkOtqDm6Ux8LX5-WFtkr0bH8OxE-XG

[@usernameispassword4023]

Thank you so much ma'am!

[@granthill5263]

Thank you so much!

[@sanjaykumarsinha3058]

The video was very informative! But i don't understand one thing. We know, if the random variable is continuous then probability at a particular point is zero.(The reason is we don't cover any area and integration is simply area under curve). But while calculating conditional pdf we take it as a non zero value. { fy(1)= .5, let's say}.Why is that?

[@Stats4Everyone]

Hi Sanjay - Good question - the answer to this question has to do with the difference between a discrete and continuous distributions. When y is discrete (say Y = 1 for a Head on a coin, and Y = 0 for a Tail on a coin), the marginal distribution of y evaluated when Y = 1 maybe non-zero. This is because fy(1) is defined to be Pr(Y=1), and if y is discrete, the probability that Y=1 is 0.5 in this example. However, if y is continuous, as in the example in this video, fy(1) = 0 (it does not equal 0.5... it must always be zero when y is continuous). Notice, in this video, I never found the probability Y = 1... in other words, I never evaluated fy(1). Evaluating Pr(Y=1) to find a conditional probability is possible when y is discrete.... though when Y is continuous, we do not find Pr(Y=1), rather we directly find the conditional distribution fx|y by finding the marginal of y and then plugging in the value of y while integrating over x... image we have a two dimensional curve -- the conditional probability is a slice of that two dimensional curve at a particular value of y .

[@tulikamal]

Thanks for the video

[@mahsan151]

Hello- your videos were very helpful in understanding conditional joint PDF. Can you please share how to solve if the question was something like: P(X>1lY>1)? Thanks

[@Stats4Everyone]

Great question! This video is similar to the example you posted: kzbin.info/www/bejne/eHOzhICClMSbhdE

[@gerardoelizondo9182]

THank you!!

[@kahlanfaiq1510]

keep up the good work :-)

[@AdrianQuevedoperfil]

thanks Michelle!

[@danialdunson]

that was awesome!

[@yutikasingh5443]

Thank you!!

[@tvvt005]

8:14 hi, if instead of a specific value, if it were given Y

[@fadikhattar290]

Im in love

[@zubairhasany4092]

how you converted into 3 parts the integral parts?

[@alinazainab8656]

Thank you so much ❤️

[@Stats4Everyone]

You’re welcome 😊 Happy to hear you found this video helpful

[@tommyharyanto7935]

thank you

[@rheabali7691]

how would we evaluate the conditional probability when y is "less than/equal to" say 1 instead of equalling 1?

[@EWB438]

P(Y

[@Stats4Everyone]

I know its been a while since you posted this question, though it is a really good one, so I made a video that might help with this concept: kzbin.info/www/bejne/eHOzhICClMSbhdE .......if this is too late for you, maybe it might help someone else with the same question. thanks for posting this comment!

[@rakeshkumar-jw5lb]

first u took good example with good explaitions

[@rakeshkumar-jw5lb]

so it is good to all

[@JeanAlesiagain3]

You are good. Thank you

[@Stats4Everyone]

Happy to hear you found this video to be helpful! :-)

[@harshitarathore7618]

It's helpful ❤️

[@Stats4Everyone]

Glad you found this video helpful! :-)

[@DD27_27]

Thank you so much

[@sheetalkumar4579]

why is the first part of the integral -> -inf to y for f(x,y)dx = 0 ? Shouldn't it be integrated in that range ?

[@Morphine-691]

❤️❤️👌😊👍🔥

[@tsunhimwong5520]

I don't know when should we use integration?

[@Stats4Everyone]

For all continuous distributions. See how for this distribution, x and y are between 0 and 2 --- so for example, x could be 1.22222 and y could be 0.3333 ... here x and y are continuous, so we use integration. If x and y could only take discrete set of values, then we would use a sum rather than integrate.

[@dianal6086]

What would be the answer for P(X>1|Y=1.5)? Would the integral bound for the conditional prob. be between 1.5 and 2 instead of 1 and 2?

[@Stats4Everyone]

The answer would still be one, since x must be more than y, and you are saying that y now is 1.5. The way the steps would change, is we would plug in y=1.5 instead of y=1. the bounds for the non-zero part of the integral would be from 1.5 to 2 ... as you said.

[@wondebest9973]

my love how are you?

[@johnsonokeyo545]

👍

[@sln7736]

what if (x>1|y>1)? how we find it?

[@niveyoga3242]

Did you watch it at 1.25x too as in the other video ^^

[@Stats4Everyone]

I know its been a while since you posted this question, though it is a really good one, so I made a video that might help with this concept: kzbin.info/www/bejne/eHOzhICClMSbhdE .......if this is too late for you, maybe it might help someone else with the same question. thanks for posting this comment!

[@ackronymm]

thank you so much)

[@birrawat8856]

we need definetion of joint probability distribution please give me clear definetion

[@ActualDayZGod]

In this video, she actually discussed 2 somewhat different mateiral. the first one is the joint probability distribution (the marginal and joint distribution). and the 2nd one is conditional distribution of the joint probability distribution. The joint probabilty distribution (f X,Y (x,y)) is basically a way to express a joint events (2 or more events) which is observed simultaneously in purpose to find their behaviour and relationship. Most times, the random variables are connected, but when they are not connected to each other, we call them independent variable. Which we can say the outcome of an event from the joint events will not affect other events in the joint events. So in short, joint distributions would be useful to describe the probability of 2 or more events happening simultaneously (which they might or might not be independent to one another). Damn I know im not explaining stuffs clear here,(atleast i tried) but at this point i just realized it is just too many things to mention. So probably i will stop trying to explain in detail and I suggest you can search stuffs online. try searching: - joint probability distribution (IMPORTANT please be clear the difference regarding independency, this will help a lot in calculation and an unclear understanding will confuse you a lot) - marginal distributions - Conditional probablity and its properties (like expected value and stuffs) - multivariable integration (this is not neccessary, but might come handy in integrating multivariable integrals. This mostly used to find marginal distributions, etc.), probably what you wanna pay attention to is how to set the lower and upper bound of the integration since it is a bit tricky sometimes. - Last, this is just an optional. If you wanna find out the "relationship" of the random variables, you can learn yourself covariance (Cov(X,Y)) and coefficient of Correlation. Hope this help even if just a bit.. no one be salty please. And sorry if I type or explain anything wrong, im no expert.

[@munyaradzindumeya5444]

obrigado

[@albertosafra4003]

What program is she writing on anyone know?

[@Stats4Everyone]

I think I used SmoothDraw for this video. I also really like OneNote.

[@ActualDayZGod]

nice video, thanks

[@WmsFootball30]

Good work through, would have been better if the problem wasn't intuitively obvious as to what the answer was though.

[@Stats4Everyone]

yeah, I agree. sometimes its nice going through the steps and showing that intuition is actually correct.