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$F=\left({\frac 1\theta}\right)^n\cdot e^{\sum_1^n x_i/\theta}$ Taking logarithm, get $-n\ln\theta-\sum_1^n x_i/\theta$ Why do we get a minus sign in the second expression before the summation?

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    Why *do* you have a minus sign there? Did you read this somewhere? If so, where?2012-12-07

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This looks like a joint density (or Likelihood) for $n$ iid Exponential random variables. If that is the case, then your first expression has a typo: there should be a minus sign before the sum in the exponent, and that's where the minus sign in the second expression comes from.