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1. Suppose that
Y
have the pdf:
f
Y
(
y
) =
(
2(
θ

y
)
θ
2
,
0
< y < θ
0
,
otherwise
(a) Show that
Y
θ
is a pivotal quantity.
(b) Find the cdf of
Y
θ
.
(c) Use (a) to ﬁnd a 90% conﬁdence interval for
θ
.
2. Suppose that the random variable
Y
has a Gamma distribution with parameters
α
= 2 and an unknown
λ
.
(a) Show that 2
λY
has a
χ
2
distribution with 4 degrees of freedom.
(b) Use (a) to derive a 95% conﬁdence interval for
λ
.
[Hint: Lecture Notes, Ch16, p.80, item 6 and p.83, item 2.]
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This note was uploaded on 03/11/2011 for the course STA 506 taught by Professor Lisa during the Spring '11 term at West Chester.
 Spring '11
 lisa

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