SticiGui:
The
Multinomial
distribution
and
the
ChiSquared
Test
for
Goodness
of
Fit
The
Multinomial
Distribution
and
the
ChiSquared
test
for
Goodness
of
Fit
Problem
1
Consider
dealing
a
hand
of 3
cards
from
a
well
shuffled
standard
deck
of
playing
cards.
Let
X1
be
the
number
of
Aces
in
the
hand;
let
X2
be
the
number
of
sevens
in
the
hand;
and
let
X3
be
the
number
of
cards
in
the
hand
that
are
neither
Aces
nor
sevens.
The
random
variables
{X1,
X2,
X3}
have
a
multinomial
joint
distribution.
(Q1)
m
Problem
2
Consider
drawing
4
cards
at
random
with
replacment
from
a
standard
deck
of
playing
cards.
For
this
problem, consider
Aces
to
be
face
cards,
not
numbered
cards.
Which
of
the
following
sets
of
variables
have
a
multinomial
joint
distribution?
(select
all
such
sets)
?
the
number
of
kings
drawn,
and
the
number
of
other
cards
drawn
m
the
number
of
spades
drawn,
the
number
of
hearts
drawn,
and
the
number
of
diamonds
drawn
the
number
of
kings
drawn,
the
number
of
hearts
drawn,
and
the
number
of
twos
drawn
the
number
of
face
cards
drawn,
the
number
of
evennumbered
cards
drawn,
and
number
of
oddnumbered
cards
drawn
(@2)
the
number
of
face
cards
drawn,
the
number
of
kings
drawn,
and
the
number
of
other
cards
drawn
Check
Answer
Problem
3
A
bowl
contains
30
balls
of
various
colors:
color
turquoiseumberlwhitelgraylluschial
ballsinbow
5

8

6
5
6

Consider
drawing
a
random
sample
of
size
8
with
replacement
from
the
bowl.
Fill
in
the
following
table
of
expected
values
of
the
numbers
of
balls
of
each
color
in
the
random
sample.
Fill
in
the
expected
values
color

turquoise

umber

white

gray

fuschia

expected
number(Q3)
1.33
@4
213
?@s)
1.6
2
@e)
1.32
@7
159
il
Consider
the
following
possible
outcome
of
drawing
the
random
sample:
color
(urquoiseumberwhitelgraylfuschial
ballsinsamplel
0

3

30
2

The
probability
of
this
outcome
is
(Q8)
0.0034
m
The
chisquared
statistic
for
this
outcome
is
(Q9)
4.31
m
Is
the
chisquare
curve
with
4
degrees
of
freedom
a
good
approximation
to
the
probability
histogram
of
the
chisquared
statistic
for
a
random
sample
of
size
8
with
replacement
from
this
bowl?
(Q10)
m
Problem
4
The
area
under
the
chisquare
curve
with
22
degrees
of
freedom
from
15.4
to
35.3
is
(Q11)
0.81
m
The
40%
percentile
of
the
chisquare
curve
with
22
degrees
of
freedom
is
(Q12)
19.76
m