1. ## joint Probability density

If the joint probability density of X and Y is given by f(x,y) =
{2 for x > 0, y > 0, x + y < 1
{0 else,
then find P(X + Y > 2/3) and P(X > 2Y).

I used an integral formula to find F(x,y) = 1/2. Is this applicable in any way? Much appreciated

2. Originally Posted by noles2188
If the joint probability density of X and Y is given by f(x,y) =
{2 for x > 0, y > 0, x + y < 1
{0 else,
then find P(X + Y > 2/3) and P(X > 2Y).

I used an integral formula to find F(x,y) = 1/2. Is this applicable in any way? Much appreciated
Did you draw the diagrams?

P(X + Y > 2/3) can be found using simple geometry. I get $2\left(\frac{1}{2} - \frac{4}{18}\right) = \frac{5}{9}$.

P(X > 2Y) can be found using simple geometry. I get $2 \left( \frac{1}{2} \cdot 1 \cdot h \right)$

where h is the y-coordinate of the intersection point of y = x/2 and y = 1 - x.

3. what do you mean by "F(x,y) = 1/2"?

4. Originally Posted by matheagle
what do you mean by "F(x,y) = 1/2"?
That was a misprint on my part. F(x, y) = 1/2 when P(X<= 1/2, Y<= 1/2)