# Thread: How do we know the area of non shaded region in bivariate continuous uniform problem?

1. ## How do we know the area of non shaded region in bivariate continuous uniform problem?

picture inserted

2. ## Re: How do we know the area of non shaded region in bivariate continuous uniform prob

seriously?

the width of the nominal rectangle is 20 units
the height is 15

the nominal rectangle has area of 300 units

we subtract off a right triangle with base and height of 5 units

this triangle has area of 25/2 units

The resulting area is 300- 25/2 = 287.5 units

Divide this by the total area of 300 units and you get

p = 287.5/300 = 0.95833333 i.e. 0.96, choice (e)

3. ## Re: How do we know the area of non shaded region in bivariate continuous uniform prob

I just don't understand how we come to the conclusion that the base and height we want to subtract is of 5 units.

4. ## Re: How do we know the area of non shaded region in bivariate continuous uniform prob

Originally Posted by math951
I just don't understand how we come to the conclusion that the base and height we want to subtract is of 5 units.
Oh. Totally different question.

In general what you're looking at here is the probability that Emily gets to the post office before the mailman collects the letters.

If she gets there before 8:15 it's a sure thing.

But between 8:15 and 8:20 the possibility exists that the mailman gets there first.

As both are on uniform distributions the probability that one arrives earlier than the other is 50/50. Hence the slope of 1 on the bit that's cut off.

That's where the 2 5's come from.

5. ## Re: How do we know the area of non shaded region in bivariate continuous uniform prob

The area of a triangle is "1/2 base times height". The unshaded region is a right triangle with legs of length 5. The base and height are both 5.