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I am reviewing old exercise solutions and the following info is given: Assume that the conjugate prior for θ (as a special case of the gamma distribution) is following the exponential distribution with E[θ] = 2.

When finding the posterior they've used a prior proportional to $\exp(-\frac{1}{2} \theta)$. How does one conclude that?

From wikipedia I find that: enter image description here

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    $\begingroup$ An exponential distribution with mean $2$ has rate $\frac12$ and density $\frac12\exp(-\frac12 x)$. Th question says this is the prior distribution for $\theta$ and uses the word "proportional" $\endgroup$
    – Henry
    May 26, 2022 at 15:10
  • $\begingroup$ I see, so the 1/2 infront of the exp() is noted as a constant and thus not affecting $\theta$. Thank you very much! :) $\endgroup$
    – OLGJ
    May 26, 2022 at 17:19

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