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Math Help - uniform probability distribution

  1. #1
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    uniform probability distribution

    Goodmorning MHF!
    New day, new questions...
    Thanks in advance for all the help you are giving me.

    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.
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  2. #2
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    Do not square that number. Double it!
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  3. #3
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    Quote Originally Posted by Plato View Post
    Do not square that number. Double it!

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

    Why shall I sum them (since they're equal)?
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  4. #4
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    Quote Originally Posted by 0123 View Post
    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).
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  5. #5
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    Quote Originally Posted by Plato View Post
    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
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