# uniform probability distribution

• Nov 4th 2007, 02:06 AM
0123
uniform probability distribution
Goodmorning MHF!
New day, new questions...

Now the question:
There is a stretch of river 4 miles long. Uniform continuos distribution.
X denotes the distance in miles of an emergency from the point zero of this stretch of river. The density function is

.25 for 0<x<4
0 otherwise

The rescue team base is at the midpoint of this stretch of river. Find the probability that a given emergency arises more than 1.5 miles away from this base.
-----
I did F(4)- F(3.5) and then I thought I could square becasue the emergency can happen from one side or the other independently. But the result is not that on the book.:(

Thank you a lot.
• Nov 4th 2007, 04:58 AM
Plato
Do not square that number. Double it!
• Nov 4th 2007, 06:02 AM
0123
Quote:

Originally Posted by Plato
Do not square that number. Double it!

Why? I thought that
independent?----> multiply!

Why shall I sum them (since they're equal)?
• Nov 4th 2007, 07:52 AM
Plato
Quote:

Originally Posted by 0123
Why? I thought that
independent?----> multiply! Why shall I sum them (since they're equal)?

Because it is an OR! It is not an and.
The event happens in [0,0.5] OR in [3.5,4].
Those are disjoint so $P\left( {[0,0.5] \cup [3.5,4]} \right) = P\left( {[0,0.5]} \right) + P\left( {[3.5,4]} \right)$.
• Nov 4th 2007, 10:00 AM
0123
Quote:

Originally Posted by Plato
Because it is an OR! It is not an and.
The event happens in [0,0.5] OR in [3.5,4].
Those are disjoint so $P\left( {[0,0.5] \cup [3.5,4]} \right) = P\left( {[0,0.5]} \right) + P\left( {[3.5,4]} \right)$.

Oh.. I see. thank you so much