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Math Help - Stuck on Exponiental Distribution

  1. #1
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    Stuck on Exponiental Distribution

    Hi there, I'm struggling to understand how to do this as my teacher thinks it fine to not teach us and just give us lecture notes instead. I can understand the normal distribution but not the exponiental, any help will be greatly aprecciated.

    I don't understand the formula, what is the e?

    The example my teacher gave me is 'a computer monitor lasts 10 years before developing a fault, the average number of failures is 1 every 10 years, so 0.1 probability of a failure a year.

    Then using exponiental distibutution she comes out with a figure of 0.3935, which I don't really have a clue as to how to do it.

    I'lld love any help, thanks.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by innerdragon View Post
    Hi there, I'm struggling to understand how to do this as my teacher thinks it fine to not teach us and just give us lecture notes instead. I can understand the normal distribution but not the exponiental, any help will be greatly aprecciated.

    I don't understand the formula, what is the e?

    The example my teacher gave me is 'a computer monitor lasts 10 years before developing a fault, the average number of failures is 1 every 10 years, so 0.1 probability of a failure a year.

    Then using exponiental distibutution she comes out with a figure of 0.3935, which I don't really have a clue as to how to do it.

    I'lld love any help, thanks.
    well, i'm not sure what "exponiental distibutution" refers to, it sounds like something from probability or statistics, but e is just a natural constant, like pi. it is an irrational number where:

    e = 2.71828183....

    it is on any scientific calculator, so i suppose you just plug it into whatever formula you use for exponiental distibutution and you will get the answer your professor did
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  3. #3
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    Cool, so e is always the same then? Thanks though thats a great help, solved a big part of my problem.

    So I was given 1- e with (-0.1x5) above e = 0.3935, which is confusing. So obviously 0.1x5 = -0.5, but as it's above the e, do I do 2.71828183 to the power of 0.5?

    Thanks
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by innerdragon View Post
    Cool, so e is always the same then? Thanks though thats a great help, solved a big part of my problem.

    So I was given 1- e with (-0.1x5) above e = 0.3935, which is confusing. So obviously 0.1x5 = -0.5, but as it's above the e, do I do 2.71828183 to the power of 0.5?

    Thanks
    1 - e^{-0.1*5}

    = 1 - e^{-0.5}

    = 1 - 1/e^{0.5}

    = 1 - 1/sqrt{e}

    = 1 - 1/1.64872

    = 1 - 0.606531

    = 0.39347

    -Dan
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by innerdragon View Post
    Hi there, I'm struggling to understand how to do this as my teacher thinks it fine to not teach us and just give us lecture notes instead. I can understand the normal distribution but not the exponiental, any help will be greatly aprecciated.

    I don't understand the formula, what is the e?

    The example my teacher gave me is 'a computer monitor lasts 10 years before developing a fault, the average number of failures is 1 every 10 years, so 0.1 probability of a failure a year.

    Then using exponiental distibutution she comes out with a figure of 0.3935, which I don't really have a clue as to how to do it.

    I'lld love any help, thanks.
    The exponetial distribution is a probability distribution with density:

    p(x; lambda) = lambda e^{-lambda x}

    and cumulative distribution:

    P(x; lambda) = 1 - e^{- lambda x}, x >= 0

    P(x; lambda) = 0, x < 0.

    Where "e" is the base of natural logarithms (the same "e" that appears in the
    normal distribution density ~=2.718), and ^ denotes raising to a power for
    example we would write x^2 for x squared, or x^y for x raised to the power y
    (which need not ne an integer).

    This distribution is used for the time between events which are random
    in time, such as the interval between of time to failure of a peice of
    equipment, or the wait for the next customer to arrive in queing models.

    RonL
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