Question: Assume our data Y given X is distributed Y | X = x Geometric(p = x) and we chose the prior to be X
Assume our data Y given X is distributed Y | X = x ∼ Geometric(p = x) and we chose the prior to be X ∼ Beta(α,β). Refer to Problem 18 for the PDF and moments of the Beta distribution.
a. Show that the posterior distribution is Beta(α +1,β +y −1).
b. Write out the PDF for the posterior distribution, fX|Y (x|y).
c. Find mean and variance of the posterior distribution, E[X|Y ] and Var(X|Y ).
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Part a To show that the posterior distribution is Beta 1 y 1 we can use Bayes theorem PX Y PY X PX P... View full answer
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