Stat 5102 (Geyer) Spring 2012
Homework Assignment 6
Due Wednesday, March 7, 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.
61.
Suppose
X
1
,
X
2
,
. . .
,
X
n
are IID Exp(
λ
). Find the likelihood function
and log likelihood function.
62.
Suppose
X
1
,
X
2
,
. . .
,
X
n
are IID Geo(
p
). Find the likelihood function
and log likelihood function.
63.
Suppose
X
1
,
X
2
,
. . .
,
X
n
are IID Cauchy(
μ, σ
), where both
μ
and
σ
are unknown parameters.
Find the likelihood function and log likelihood
function.
64.
Suppose
X
1
,
X
2
,
. . .
,
X
n
are IID Laplace(
μ, σ
), where both
μ
and
σ
are unknown parameters.
Find the likelihood function and log likelihood
function.
65.
Suppose
X
1
,
. . .
,
X
n
are IID Exp(
θ
) and
Y
1
,
. . .
,
Y
n
are IID Exp(1
/θ
)
and the
X
’s and
Y
’s are independent of each other.
Find the likelihood
function and log likelihood function.
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 Spring '03
 Staff
 Derivative, Laplace, Maximum likelihood, log likelihood, MLE.

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