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UA / Statistics / ST 260 / How do we measure uncertainty?

# How do we measure uncertainty? Description

##### Description: This is part 1 of chapter 5. I'll upload the second part on friday morning after the lecture. These notes include examples that are broken down. You won't find these examples on the power point.
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ST 260

## How do we measure uncertainty?

Chapter 5 Note. Part 1 – 2/10/14

Prof. Cali Davis

Quick Recall:

­ Quantitative Variables: differences that have meaning to them, such as age, income,  height, and weight.

­ Qualitative Variable (OR categorical): putting people or things into classifications. Such  as: gender, race, occupation, country, or political affliction.

Statistics can be described as “the science of decision­making in the face of uncertainty”  (An educated guess)

So how do we measure uncertainty?

­ Using probability: A numerical value or measure of the LIKLIHOOD that a certain  outcome or event occurs.

P(A)= probability of eventA

­ Probability requirements for discrete variables:

0 less than or equal to P(A), which is also less than or equal to 1

## What is the probability of a customer defaulting?

So P(A) is between 0 and 1

The way we look at what 0 is and what 1 is:

P(A) = 0 impossible event

P(A) = 1 certain event

**Sum of the probabilities of all possible outcomes must equal one (1)** Example: if the probability that the broncos win the super bowl is half

(50%), and the probability that the panthers win the super bowl is half (50%), than the  sum of the probabilities equals 1 (100%).

½ + ½ = 1

Probability can be conditioned under certain circumstances Don't forget about the age old question of What is hernando de soto famous for?

Conditioned Probability: The chance one event happens, given that another event will  occur.

Example: if the broncos when the super bowl, the bars will probably sell more alcohol.

## What is the probability of a customer defaulting given that he fails test a?

Example: if the panthers win the super bowl, the broncos’ fans will probability  start a riot.  We also discuss several other topics like What was the primary purpose of the telecommunications act of 1996?

P(A | B) =P(A and B)/ P(B)

= All outcomes belonging to BOTH A AND B

Divided By

Those outcomes in the restricted group, B

Example Problem: (Cali Davis lecture) Credit Card Manager

­ New credit test to determine credit worthiness. Credit test checked against 500 previous  customers.

CREDIT TEST A

Credit History:

Passed (P)

Failed (F)

350

50

20

80

Don't forget about the age old question of What does people are rational mean?

370 130

Good (G) ­1st row

Default (D) ­2nd row

1st row = total 400

2nd

row = total 100

Total both rows = 500

What is the probability of a customer defaulting?

­ 80 people failed and defaulted.

What is the probability of a customer defaulting given that he fails test A?

­ General rules

P(A and B) = P(A) ∙ P(B|A) If you want to learn more check out How we study the brain?
If you want to learn more check out What was the main reason for the english civil war of 1642?

= P(B) ∙ P(A|B)  Don't forget about the age old question of How you put together a speech?

P(A or B) = P(A) + P(B) ‐ P(A and B)

Look at the part

that overlaps

Does knowledge from test A help you make a better decision?  P(D)= .20

P(D/F)= .62

Do you want to know the test A results before you give the loan?  “Credit test A results” and “defaulting” are dependent variables.

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