Class notes
Homework
- Course
- 3081
- Institution
- Northeastern University
Lecture notes of 1 pages for the course 3081 at Northeastern University (Homework)
[Show more]
Seller
Follow
Content preview
MATH 3081 Homework 5 .Name:
3.2.4 An entrepreneur owns six corporations, each with more than $10 million in assets. The entrepreneur consults the
U.S. Internal Revenue Data Book and discovers that the IRS audits 15.3% of businesses of that size. What is the
probability that two or more of these businesses will be audited?
C
more) &
n = G PlAudit Cor more) + P(Auditz or =
more)
p(Ardit
2 or
:.
153 1. p[Ardit 1) -
p(Audito) =
p
1 ,2
1) binpdf (6 153 01) =
P(Audit or worel
(binpdf[6 153
..
:
X + ,
I -
.. ,
=
.
231 =
O 23 1 %
.
3.2.7 Doomsday Airlines (“Come Take the Flight of Your Life”) has two dilapidated airplanes, one with two engines,
and the other with four. Each plane will land safely only if at least half of its engines are working. Each engine on
each aircraft operates independently and each has probability p = 0.4 of failing. Assuming you wish to maximize
your survival probability, which plane should you fly on?
PCLive) :
p(2 or more engine 2
= ↑
PCLive) p(lor engine) n : 2
:. Y
: more
p
P =. 4
1 -
P(0) = p(live)
pllive) = /- p(d) 4 0) 87
1-binpdf (4 , . ,
=.
I-binpdf (2 4 0) =. 64
give
=
.. ,
ble 87 % of living
plane
3.2.8 Two lighting systems are being proposed for an employee work area. One requires fifty bulbs, each having a
probability of 0.05 of burning out within a months time. The second has one hundred bulbs, each with a 0.02
burnout probability. Whichever system is installed will be inspected once a month for the purpose of replacing
burned-out bulbs. Which system is likely to require less maintenance? Answer the question by comparing the
probabilities that each will require at least one bulb to be replaced at the end of thirty days.
n = 50 piloc less maintenance
02
Pi .
05 n =.
o a
PCat least (bulb) = 1-biapdf (50 ,.
05 ,
Platleast (bulb) :
1-binpdf
(100 .
02 ,
= 92 3 % it needs %
= 86 7
replacing
.
.
replacing
3.2.9 The great English diarist Samuel Pepys asked his friend Sir Isaac Newton the following question: Is it more likely
to get at least one 6 when six dice are rolled, at least two 6s when twelve dice are rolled, or at least three 6’s when
eighteen dice are rolled? After considerable correspondence [see (158)]. Newton convinced the skeptical Pepys
that the first event is the most likely. Compute the three probabilities. Newton is
always right
nies
12
18
n = n :
L-binpdf (6 ,
" e
p : TG p
:
G
I
/ q 3
q 9:
= 2 > :
O66 3 1 p(x) p(i) p(d) p() p()
-
- - -
.
1 -
1- 112 - 764 135 .. 23
1
.
0376
. -
-
·
.
.
=
Co
. % 59 7
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller maxlangweil. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
80364 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now