Probability question, joint probability distribution
Sailboat's route on map is 6km long. Because of the weather, the real traveled distance of the boat is random variable X (km) and speed Y (km/h). Density functions and sample spaces of these two independent random variables below.
$f(x)=\frac{x6}{2}, \Omega_x=[6,8], $
$g(y)=\frac{y}{8}, \Omega_y=[3,5]$
What's the probability that the boat arrives to the destination in under 2 hours? (hint: draw a picture of the sample space and events, and choose bounds for the integrals from the picture)
Note: I only need the initial integral with bounds and the final answer.

Uhm, I assume the distance is uniform between 6 and 8, and the speed is uniform between 3 and 6, but I don't understand what f and g are.
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This took me over 30 minutes to answer. Please offer higher bounties for your future posts, specially if you have a short deadline.

There was a mistake in computing the double integral. I just fixed it.

This doesn't turn out correct either, which is weird.

Did you go through my solution? The solution seems fine to me. That's how the problem should be done.

Yeah, I went through your solution, checked everything, and I even went ahead and integrated in order dydx. Got the same answer. Must be a glitch in Moodle :). Do you happen to know if I can close the dispute somehow, this was my first time here, hope you didn't get offended haha.

I believe the disputes can not be revered. But since we are in agreement, the judge has an easy decision to make.

OK, I finally got the right answer. My hunch was right, your h(x,y) was wrong. h(x,y) was in fact f(x)*g(y). This was then integrated first from x/2 to 5, with respect to y, and on the outside from 6 to 8 with respect to x. This gives us 23/32=0.71875. But to make the judges' lives easier and to not provoke you any further, I let the judges take my $10 and give it to you for the time and effort you put in your solution. Have a nice weekend :)

The statement of the problem is not clear then. Note that the arrival time =distance/speed. So it makes more sense to have h=f/g.
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