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

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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. That’s 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 Austin’s 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 Austin’s 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

Austin Menger

STAT 1100Q

2

c. (2 points) Find the probability that Taylor Swift is Austin’s favorite

music artist or Austin will go to a Taylor Swift concert.

d. (2 points) What is the probability that Taylor Swift is Austin’s

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 Austin’s 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

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