# Math Help - Simple question need answer #2

1. ## Simple question need answer #2

2. Given the density f(x,y)=2(x+y), 0<x<1, 0<y<x, calculate
a) P(X<0.5, Y<0.5)
b) P(X<0.5)
c) P(Y<0.5)

Thanks~

2. 2a)

$
\int_{0}^{a}\int_{0}^{x}2\cdot(x+y)\;dy\;dx\;=\;\f rac{1}{2}
$

Solve for 'a'.

3. ## what's the difference between 2a and 2b?

what's the difference between 2a and 2b in this case?

4. Originally Posted by ugling
2. Given the density f(x,y)=2(x+y), 0<x<1, 0<y<x, calculate
a) P(X<0.5, Y<0.5)
b) P(X<0.5)
c) P(Y<0.5)

Thanks~
a. $\int_{x = 0}^{x = 1/2}\int_{y = 0}^{y = x}2 \cdot (x+y)\; dy \; dx$

b. Same as above.

c. $\int_{y = 0}^{y = 1/2}\int_{x = y}^{x = 1}2 \cdot (x+y)\; dx \; dy$

In each case it helps to draw the required region of integration to get the integral terminals.

5. Originally Posted by TKHunny
2a)

$
\int_{0}^{a}\int_{0}^{x}2\cdot(x+y)\;dy\;dx\;=\;\f rac{1}{2}
$

Solve for 'a'.
So, I'm just making up my own problems, today. Sorry about that.

6. Originally Posted by TKHunny
So, I'm just making up my own problems, today. Sorry about that.
It's a good question though

7. Originally Posted by ugling
what's the difference between 2a and 2b in this case?
shakespeare
2b or not 2b