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Stat 5102 (Geyer) Spring 2012
Homework Assignment 9
Due Wednesday, April 11, 2012
Solve each problem. Explain your reasoning. No credit for answers with
no explanation. If the problem is a proof, then you need words as well as
formulas. Explain why your formulas follow one from another.
91.
Suppose
X
is Bin(
n,p
) and the prior distribution for
p
is ﬂat (a proper
prior, since
p
is bounded).
(a) Find the posterior distribution for
p
.
(b) Find the mean of the posterior distribution for
p
.
(c) Find the standard deviation of the posterior distribution for
p
.
(d) Find the mode of the posterior distribution for
p
.
(e) In the case
x
= 0,
n
= 10, ﬁnd the posterior median for
p
.
92.
Suppose
X
1
,
...
,
X
n
are IID Exp(
λ
) and the prior distribution for
λ
is ﬂat (an improper prior). The posterior distribution for
λ
was found in
problem 810 (a).
(a) Find the mean of the posterior distribution for
λ
.
(b) Find the standard deviation of the posterior distribution for
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