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Math Help - Can this be simplified?

  1. #1
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    Can this be simplified?

    I cant figure out how to simplify the following equation, but have been told it is possible:

    ln(sum(e^(theta*z)))

    In this case z is a discrete random variable that only takes on values of 1 or 0 because it comes from a bernoulli distribution. Theta is a value that will later become maximized. How can I simplify this? I know that since z is a discrete random variable that changes some things. Thanks!
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  2. #2
    MHF Contributor

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    In general, no. ln(x+ y) does not simplify.
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  3. #3
    A Plied Mathematician
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    As HallsofIvy has said, you can't simplify anything outside the logarithm. However, if you know how many times you've got z = 0 (say, n), and how many times you've got z = 1 (say, m), then you can simplify inside the logarithm thus:

    \ln(n + m e^{\theta}).

    That's the end of the road, however.
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