Conditional Probability For X given Y is less than 1 Provided we have the Joint PDF

Find the conditional probability that X is less than 0.5 GIVEN that Y is less than 1.

[@FlipDeCoin]

This taught me in the first two minutes what my graduate-level professor was unable to teach over two days. Thanks!

[@micahross1227]

I like your style. You and Mancinelli are the best. Thank you.

[@watasn5081]

For more solved question on the Joint Probability Density function click on the link below: drive.google.com/file/d/1sEylHsFaX6aHTWjiCKaBqwaLcnfG0A7X/view?usp=sharing

[@dasellcalipay1899]

What a big help! You explained it very well. Thank you so much :)

[@arslanMCL]

Nice Video. Between which device you are using for writing on screen

[@Stats4Everyone]

For this video I was using Smooth Draw, and Wacom Bamboo Splash Pen Tablet. Though recently I upgraded my tablet to the XP-PEN Artist12 11.6 Inch FHD Drawing Monitor - I really like both of these for screen writing :-)

[@jaiicee2117]

Thank you so so much ! Ugh. Been struggling with this topic 😣

[@DPets]

Thanks!

[@michelrodriguez3603]

Thanks for the Video

[@sifatahmed1413]

Best explanation

[@ahmetkarakartal9563]

thank you so much

[@Computervirusworld]

thanks

[@reaganolguin151]

could you solve the question by factoring the joint distribution into x(2-y) which shows the two variables are independent. Then by knowing that the marginal density of X is proportional to x you find the the constant "c" which satisfies c * integral (x) from 0 to 1 =1. Then finally you integrate x from 0 to 1/2 and then multiply by to get the answer. I ask because that is what I did.

[@reaganolguin151]

Edit of last 2 sentences: Then finally you integrate x from 0 to 1/2 and then multiply by "c" get the answer. I ask because that is what I did

[@sirmexicanelmo]

What if Y=1 and not less than. I am assuming you would still have to find the marginal distribution but I don't think you would then take the integral. What would you do instead? Or would you take the integral?

[@Stats4Everyone]

This is a good question. Thank you Jaime for posting. We would start by finding the conditional distribution, fx|y = fxy / fy We found in the video that fy = 1 - 1/2 y, 0

[@058_pratiksandilya9]

@@Stats4Everyone If it is X

[@anjalisahoo650]

Let X and Y be independent random variables and both of them are uniformly distributed in [0, 1]. If the smaller (of the two) is less than 1/4, then what is the conditional probability that the larger is greater than 3/4? please solve this

[@Stats4Everyone]

Since X and Y are independent, the the probability that X is less than 1/4 does not depend on Y being greater than 3/4.... In other words: Pr(X < 1/4 | Y > 3/4) = Pr(X < 1/4) since X is independent of Y. To find Pr(X < 1/4) use the uniform distribution and integrate from 0 to 1/4... Let me know if this makes sense, or if you have any follow-up questions

[@sat1sh45]

You're amazing

[@rakeshky1000]

can u please help me how to do for exponential function with x and y

[@Stats4Everyone]

Can you clarify this question. What does the joint pdf look like? Also, what is the probability you are looking to solve?

[@viajeespacial5391]

Thanks