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PSTAT 120C:
Assignment #4
Due May 14, 2009
1. Suppose that we know that of the large ﬁsh in a lake the species are 40% perch, 35% bass and
25% trout.
(a) What is the probability that a random sample of 5 large ﬁsh contains 2 perch, 2 bass,
and 1 trout?
(b) What is the probability that a random sample of 4 large ﬁsh will have more trouts than
bass?
2. Suppose that
X
1
,X
2
,X
3
,X
4
are multinomially distributed with
n
= 16 and
p
1
=
ab
p
2
= (1

a
)
b
(1)
p
3
=
a
(1

b
)
p
4
= (1

a
)(1

b
)
(2)
for some
a
and
b
between 0 and 1. Let
S
=
X
1
+
X
2
and
R
=
X
1
+
X
3
.
(a) Find
P
{
R
= 10
}
.
(b) Find the
P
{
X
1
= 6

S
= 12
}
.
(c) Suppose we want to condition on the event
{
S
= 12
,R
= 10
}
, what are the possible
values that
X
1
can take?
(d) Find
P
{
X
1
= 0

S
= 12
,R
= 10
}
.
3. A gambler wants to test whether the die she has is fair so she rolls it 300 times and records
the outcomes as
Roll
1
2
3
4
5
6
Count
54
71
42
45
51
37
meaning she rolled a 1 on the die 54 times, etc.
(a) A fair die has probability 1/6 for each of the six outcomes. Use a chisquared test to test
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This note was uploaded on 10/02/2009 for the course PSTAT 5E taught by Professor Eduardomontoya during the Spring '08 term at UCSB.
 Spring '08
 EduardoMontoya

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