Need help with my homework problem , most of the code is provided on the last page please 1
Hoomework
3
Name_______________________________
NOTE
: All work associated with a given problem part MUST be placed DIRECTLY beneath that part.
Problem 1 (20pts)
In an article concerned with smokers and people who are obese it is stated that: 23.5% are obese,
22.7% of Americans are smokers, and 4.7% are both obese and smokers.
http://www.bmj.com/cgi/reprint/333/7557/25
In probabilistic terms, it should be clear that the generic 2D random variable of interest in this study is (
O,S
):
where
?
O
”
The act of recording whether the person is not
[
O
=0],
or is
[
O
=1]
obese
”
and
S
=”
The act of recording whether the person is not
[
S
=0],
or is
[
S
=1]
a smoker
”
Clearly, the sample space for
)
,
(
S
O
is:
?
)
,
(
S
O
S
{ (0,0) , (1,0) , (0,1) , (1,1) }.
(a)(4pts)
Give the single subset of
)
,
(
S
O
S
that correspond to each of the following events in relation to any person:
Answer
[= No need to show work]:
(i) “The event that the person is obese”:
?
?
]
1
[
O
(ii) “The event that the person is a smoker”:
?
?
]
1
[
S
(iii)“The event that the person is obese and a smoker”:
?
?
?
?
]
1
1
[
S
O
(iv)”The event that a person is obese, given that person is a nonsmoker”:
?
?
?
]
0

1
[
S
O
(b)(7pts)
For each singleton set {(o,s)}, let
)}
,
Pr{(
s
o
p
os
?
?
. From the reported results, obtain numerical estimates
for the
four singleton set probabilities :
11
01
10
00
,
,
,
p
p
p
p
. Denote these estimates
as
11
01
10
00
,
,
,
p
p
p
p
?
?
?
?
.
Solution
[= Show work]:
(c)(3pts)
In the article it is also stated that “41.5% of adults in the US are either obese or smoke”. Use your results in (b)
to verify this number. [Hint: Identify the event
]
1
1
[
?
?
?
S
O
as a subset of
)
,
(
S
O
S
.]
Solution
:
(d)(4pts)
Given that a person is obese, estimate the probability that the person is also a smoker.
Solution
:
Answer