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Math Help - Conditional Expectation Problem

  1. #1
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    Conditional Expectation Problem

    I have the solution to this example, but I don't understand it. It's the third step that I don't understand.

    "For a population of individuals, you are given:

    i) Each individual has a constant force of mortality.

    ii) The forces of mortality are uniformly distributed over the interval (0,2).

    Calculate the probability that an individual drawn at random from this population dies within a year."

    Solution:


    I don't understand the third step, where the integral is split. How is the f(u) function able to disappear and get replaced by 1/2. It's been a few months since I've done a multivariable probability problem...
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  2. #2
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    Quote Originally Posted by paulrb View Post
    I have the solution to this example, but I don't understand it. It's the third step that I don't understand.

    "For a population of individuals, you are given:

    i) Each individual has a constant force of mortality.

    ii) The forces of mortality are uniformly distributed over the interval (0,2).

    Calculate the probability that an individual drawn at random from this population dies within a year."

    Solution:


    I don't understand the third step, where the integral is split. How is the f(u) function able to disappear and get replaced by 1/2. It's been a few months since I've done a multivariable probability problem...
    "The forces of mortality are uniformly distributed over the interval (0,2)" => f_M(\mu) = \frac{1}{2}. Uniform distribution: http://en.wikipedia.org/wiki/Uniform...on_(continuous)
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