Joint PDF #3 - Deriving Joint Cumulative Distribution Function from Joint PDF

[LuneriBoxilo]

Great tutorial, Definitely improved my understanding; Just wanted to say thanks!

[galinrizov]

How would we solve that same problem if our variables were defined lets say

0 < x < 5

0 < y < 4

I guess we will have more than one double integral .....Are we going to have like 4 separate cases ?

[stepbil]

@galinrizov Actually this one would be the same as example 1 in my video. so to get the probabilities that both shark attacks in year 0 to 5 and croc attacks in year 0 to 4, this is equivalent to (1-exp(-4))*(1-exp(-5)). This always applies for joint exponential distribution when the lower limits are both 0. alternatively you would need to solve a double integral just like in example 2 (with 0,0 as lower limits and 4,5 as upper limits)

[skyhao0926]

thank you so much

[vissionboarder144]

Thank you!  Very very helpful!

[vic1518]

Great videos - thank you!

[stepbil]

Oh yeah u just spotted another typo. Sorry for that ! indeed at 4.23 the result of integration should be -e^-u and not -e^-x. well spotted ! Obviously that's the price to pay for intechanging so many x's with u's & brain malfunctioning ;-) The result however is correct , if that can be of any consolation ;-)

[daphniek1]

Hi! After the integration of e^ -u dudv the result should be -e^ -u. I am confused because in the video, you had it -e^-x. Please correct me if im wrong. But the entire presentation is superb!

[imkb010]

Your videos are very well organized. All the boxes with the relevant properties and definitions are really helpful for following the steps. Thanks for sharing!!!

[themorgoth]

thanks, dude!

[stepbil]

hey rockstar1720003 . You are right there is a copy paste issue there. The second title in green should say : "From Joint CDF to joint PDF" . Thanks for spotting.

[rockstar1720003]

I think the second one is "From Joint CDF to joint PDF."