Try searching up for "double integration and limits" problems online (YouTube) and it should be much clearer
Draw the line y = 30-x (rearranging is x+y=30) on the cartesian plane. For x,y > 0, this is the first quadrant.
When you want the probability P(Y < 30-X), this is the double integral over the region bounded by the line x+y=30, x=0, y=0.
For double integrals, the outer limits are always constant whilst the inner ones depend on the next variable we integrate with respect to.
The order of integration in that integrand was dydx, so it means we integrate w.r.t y first, and then w.r.t x.
So we want to have bounds on the integral such that it "covers" this whole region (the region I first presented, which will be a triangle in the first quadrant of the plane).
If we restrict it for: 0 less than y less than 30-x and then 0 less than x less than 30 then this will cover this region we want. (see: https://www.desmos.com/calculator/nmfg4p0cw4)
I'm not sure why it keeps cutting off my message randomly.
(For some reason having inequality signs in text deletes the message...)
Last edited by kawaiipotato; 15 Jun 2017 at 7:28 PM.
Sxc avatar made by a sxc person: carrotontheground http://community.boredofstudies.org/...otontheground/
Try searching up for "double integration and limits" problems online (YouTube) and it should be much clearer
Sxc avatar made by a sxc person: carrotontheground http://community.boredofstudies.org/...otontheground/
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