Chapter 5 Note. Part 1 – 2/10/14
Prof. Cali Davis
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
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.
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
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
Don't forget about the age old question of What does people are rational mean?
Good (G) 1st row
Default (D) 2nd row
1st row = total 400
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?
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
Does knowledge from test A help you make a better decision? P(D)= .20
Do you want to know the test A results before you give the loan? “Credit test A results” and “defaulting” are dependent variables.