MA 381: Section 8.1: Joint Probability Density Functions 

3 hrs of struggle, and this video uses 30 sec to make joke of my life. 30 sec from this video is all i need.

perfect logical explanation, I wish all of my teachers explained this clearly!!

Thank you so much. You are truly a life saver. I have a deadline in 15 hours but I have no idea how to do it, nor that I have a single clue from my book. But you saved me, now I understand how to choose my bound from the picture of my support. Thank you!

This video is crystal clear.Thank you for clearing my confusion.

In example 4 why is that you didnt make use of lower limit of y=0 and upper limit of y=1 while calculating the value of k whereas range of 0 to 1 was used for x?

it helped me a lot(3 hours before the exam:)),thank you so much

you are a great professor, thank you!

what is the name of this book?

In the marginal of y How you have taken the limits fom y to 1

k/8 = 1/2 isn't it? Because The value of our area is 1/2. Could you please explain it ? Thank you so much for this helpful video

i dont get it...why didnt you do the additional part...i wasted 9:51 waiting for that part

thank you so much for this.

Really helpful! Thank you!! Could you please explain explain the following questions... P(X=x,Y=y)= c(xy+x+1) where x=0,1,2 and y=0,1. no other values are possible. (a) show that c= 1/15 makes this a valid probability distribution. (b) find the marginal distribution of X and also E (X). (c) find the conditional distribution of X given that Y=1 and evaluate it's mean.

it was helpful . thankyou so much..

Thank you for posting good lectures. It helps me a lot. btw, Click "don't show this message again"!!!

thank u very much for poSting thiS video..

Thank you for your teaching

Thank you, very straight forward!

Thank you so much this is very helpful

If you could slow down just a little it would be super helpful! I guess you are limited to a 10-minute video...

Thank you

Excellent explanation!

Thanks for your lecture. Could you please explain me for the following function. Find the value of k for the function f(x,y)=kxy^2 if 0≦x≦y≦1

thank you so much

I still don't understand😥

This is great

Anyone else try to close out the window at 1:11 thinking it was their computer?

ty

thank you