Double integration...
with x+y dy dx where y goes from x to infinity and x goes from 0 to 1/2... anybody up for this???

Question

anonymous · Answer

$$P(X \le1/2)=(I think)\int\limits_{0}^{1/2} \int\limits_{x}^{\infty} (x+y)dy dx$$

anonymous · Answer

$$\int\limits_{0}^{1/2}\int\limits_{0}^{x}(x+y)dydx$$ is your integral. Since all they gave you was the probability x is at least 1/2 or smaller,  the probability has to be between 0 and 1, so your dy limit will start at zero and go as far as x. That is just like takin the limit as x goes to infinity on the upper limit. But it does have to be at least zero by order of the definition of a probability. So you just solve that and you've got it. I got 1/64 +1/24, which is some small decimal and consistant with the definition. I'm sure you can do the integration just fine.

anonymous · Answer

Thank You!!!  the infinities were making me dizzy....

anonymous · Answer

No problem, I had to spend some time looking it up, and I almost confused myself.