STAT 1100Q Study Guide - Midterm Guide: Bayes Estimator, Random Variable, Probability Distribution

22 views8 pages
13 May 2021
School
Department
Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Austin Menger
STAT 1100Q
1
Midterm 2 Exam (Written Portion) - 1100Q Spring 2021
***Please make sure you also complete the multiple choice portion in
HuskyCT.***
Name:
ID Number:
Please round all decimals to 2 points to the right of the decimal. Relax and do
your best. Thats all you can ever ask from yourself in life.
Probability Basic Principles & Bayes’ Rule
Suggested Time: 30 minutes
Points: 27
1. The probability that Taylor Swift is Austins favorite music artist is .10. The
probability that he will go to one of her concerts is .84. However, the
probability that he does not like Taylor Swift and will go to a concert
(because his wife makes him) is .75.
a. (3 points) Write down the 3 pieces of information given in terms of
probabilities involving event A (Taylor Swift is Austins favorite
music artist) and event B (Austin will go to a Taylor Swift concert).
b. (3 points) Summarize the above information using a probability
table.
Dhrasti Patel
2566809
Event ATaylor Swift is Austin's favoritemusic artist
Event BAustin will goto Taylor Swift concert
Event CAustin goes to anotherconcert
PLA z0.10 PB084
B0.84
Aoui BO16
C0.75
Alo 9I10.25
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 8 pages and 3 million more documents.

Already have an account? Log in
Austin Menger
STAT 1100Q
2
c. (2 points) Find the probability that Taylor Swift is Austins favorite
music artist or Austin will go to a Taylor Swift concert.
d. (2 points) What is the probability that Taylor Swift is Austins
favorite music artist given that he will go to a Taylor Swift concert?
e. (2 points) Knowing that Austin will not go to a Taylor Swift concert,
what is the probability that Taylor Swift is Austins favorite music
artist?
f. (3 points) Use Bayes Rule to find the probability that Austin will go
to a Taylor Swift concert given that Taylor Swift is his favorite music
artist.
PAor BpLA UBpCA tPBPAB
But pBIA PLAID PAB PLA PBIA
PAa1LO 84 0.084
PAUB 0It084 O084
0.856
PABPAB
Mg
iO
0.84
PLAIN Pippo PH
IpfApgI.Y ooff
Ol
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 8 pages and 3 million more documents.

Already have an account? Log in
Austin Menger
STAT 1100Q
3
g. (3 points) Are event A and event B independent? Justify your
answer numerically (be exact here!).
2. We know that the probability of Taylor Swift dying her hair bright pink is
.50. Given that she has dyed her hair pink there is a 40% chance that she
is complaining about an ex-boyfriend. There is a 40% chance that she is
complaining about an ex-boyfriend.
a. (3 points) Write down the information given in terms of the
probabilities of event C (Taylor Swift dyes her hair pink) and event
D (she is complaining about an ex-boyfriend).
b. (2 points) What is the probability that Taylor Swift is not
complaining about an ex-boyfriend and she dyed her hair pink
(hint: think about using the conditional probability you’re given
here)?
c. (2 points) What is the probability that Taylor Swift is not
complaining about an ex-boyfriend and she did not dye her hair
pink (hint: can you use independence here)?
PAB O084 Independent if PLAB PEA NB
PAOvIpAPB0.1 10.84 0.084 PAB
PB0.84 ABare independent
Event CTaylor Swift dyes her hair pink
PLC O50
PDIC 0.4 Event Dcomplaining about ex boyfriend
PCD O40
pDesc PCc PcD
PCc pDg Pcc
D50 O40 050
0.3
aPDlc Pc
PCUD PCPCD pCn D
0.50 40.40 O40.5
0.7
PCon Doj I0.7 0.3
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 8 pages and 3 million more documents.

Already have an account? Log in

Get access

Grade+
$10 USD/m
Billed $120 USD annually
Homework Help
Class Notes
Textbook Notes
40 Verified Answers
Study Guides
1 Booster Class