Stat 5101 (Geyer) Fall 2009
Homework Assignment 9
Due Wednesday, November 25, 2009
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.
Parts (e) and (f) of problem 89 deferred from the preceding home
work, which see for the problem statement.
92.
Part (c) of problem 810 deferred from the preceding homework, which
see for the problem statement.
93.
Suppose
E
(
Y

X
) =
X
var(
Y

X
) = 3
X
2
and suppose the marginal distribution of
X
is
N
(
μ,σ
2
).
(a) Find
E
(
Y
).
(b) Find var(
Y
).
94.
Suppose
X
1
,
...
,
X
N
are IID having mean
μ
and variance
σ
2
where
N
is a Poi(
λ
) random variable independent of all of the
X
i
. Let
Y
=
N
X
i
=1
X
i
,
with the convention that
N
= 0 implies
Y
= 0.
(a) Find
E
(
Y
).
(b) Find var(
Y
).
95.
Suppose that the conditional distribution of
Y
given
X
is Poi(
X
),
and suppose that the marginal distribution of
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 Fall '02
 Staff
 Poisson Distribution, Probability theory, Binomial distribution, xk, conditional distribution

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