## Transcribed Text

1. Suppose that
21 45 , ,..., XXX
are independent,
Xi Poisson ο½ο±ο¬ )(~
. Find the p-value given by
the likelihood ratio test of
H0
:ο± ο½ 20
vs
H1
:ο± οΉ 20
if
18 4. ο±
Λ
MLE
ο½ .
2. Suppose that
21 72 , ,..., XXX
are independent,
i BetaX ο½ο½ ο±ο’ο‘ ),1(~
. Find the p-value given
by the likelihood ratio test of
4: H0 ο± ο½
vs
4: H1 ο± οΉ
if
5.4
Λ
ο± MLE
ο½ .
3.
21 35 , ,..., XXX
are independent,
~ )(ο±1 Xi
lExponentia , and
21 40 , ,...,YYY
are independent,
~ )(ο± 2 Yi
lExponentia . We observe
X ο½16 2.
and
Y ο½ 20 1.
. We use the likelihood ratio test of
H :
10 18 ,ο±ο± 2 ο½ο½ 18
vs
: is false. HH 01
Find the p-value.
4.
)1 ,(~
2 NormalX 1 ο³ο±ο ο½ο½ , )2 ,(~
2 NormalY 2 ο³ο±ο ο½ο½
, and
)3 ,(~
2 NormalZ 3 ο³ο±ο ο½ο½ .
X, Y, and Z are independent. We use the likelihood ratio test of
H : ο±ο±ο± 3210 ο½ο½ο½ 0
vs
: is false. HH 01
We observe
.1 80 .2, 52 ZYX ο½ο½ο½ .1, 62.
Find the p-value.
5.
ο Beta ο’ο‘ ο½ο½ )2,2(~ . X ο nBinomial ο½ ο°),2(~|
. Find
xf )(x
. Simplify algebraically.
6.
ο Beta ο’ο‘ ο½ο½ )2,1(~ . X ο nBinomial ο½ ο°),2(~|
. Find the posterior mean and standard
deviation if X = 2 is observed.
7. ο Beta(~ 32 , ο’ο‘ ο½ο½ 23)
and
X | ο½ο ο°
is
( 20 pnBinomial ο½ο½ ο°), . Find
P |5.0( X ο½οΎο 16) .
8. ο Beta(~ 10 , ο’ο‘ ο½ο½ 10)
and
X | ο½ο ο°
is
( 100 pnBinomial ο½ο½ ο°),
. We are testing
5.0: H0 ο£ο
versus
5.0: H1 οΎο
. Find
ο¨ ο© 0
| XHP ο½ 60 .
9. Suppose
f ,1)( ο°ο° οΌοΌο½ 10 , X | ο ~ Binomial(n = 3, ο°
),
Y | ο ~ Binomial(n = 2,
ο°
). Give
yf )(
y
if X = 0. Simplify your answer algebraically.
10. Ken is the best cribbage player at Hoover High. Gordon is the best cribbage player at Wilson
High. They play a three game match. Ken has probability
ο
of winning each game. If we take
f
ο°
,1)( ο°ο° οΌοΌο½ 10
, what is the probability Ken wins 2 of the 3 games if he loses the 1st game?

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.