Probability Density Function and Cumulative Distribution function

Suppose you have a random variable X and Y with Joint PDF define by: otherwise
I found K=3.
How would you find
and
matter of fact it would be nice to know what it means.
Thanks.

Re: Probability Density Function and Cumulative Distribution function

a) The probability is found by integrating over the region

in the following double integration, with the integrand as the joint pdf:

In practice of course it would be easier for you to visualize this region in the 2-D plane so that you can break it piece-wisely and translate it in terms of upper and lower limits of x and y.

b) This is a conditional pdf. You check the definition first and see if you got any difficulty.

Re: Probability Density Function and Cumulative Distribution function

visually, 2x<y just left the negative half of the dominion, that is 1/2

analitically, in the positive y<x, so 2x<y<x no chance
if x<0 then 2x<y<-x, but as 0<y<-x then you have just the second integral that gave u K=3

f()y/x = f(x,y) / f(x) -> f(x) = 3/2 x^2, you can make the integral from 0 to |x| without problem because later you have x^2, then you test f(x) from -1 to 1

then f()y/x=2 y / x^2 0<y<|x| then you test that this a prob func

i did this problem mostly because of the first part, not without some difficulties, i think i achieved a valid solution

Last edited by amilsan; 11-16-2015 at 09:03 PM.
Reason: forgot to mention f()y/x limits