Statistics 101 lecture outline: Basic probability
Statistics 101: Basic probability
Administrivia:
The solutions will appear on the web on Thursday afternoon
Example: Cats and dogs
Raise your hand if you had cats and dogs as pets growing up?
Raise your hand if you had cats or dogs as pets growing up?
This is the way to think about intersection ("and") and union ("or")
Make Venn diagram
Three types of probability:
counting (e.g. cards, coins and dice)
Psychological or subjective (e.g. horse track betting)
long run frequency (e.g. science)
All three types follow these rules:
0 <= P(A) <= 1
P(A or B) = P(A) + P(B) if A and B are mutually exclusive
P(A or B) = P(A) + P(B) - P(A and B)
P(A) = 1 - P(not A)
P(A|B) = P(A and B)/P(B)
Probabilities can often be represented as tables (did diferent example in class)
Male
Female
total
Taller than 6 foot
.2
.05
.25
Shorter than 6 foot
.3
.45
.75
Total
.5
.5
1.00
It is easy to read off P(Taller|Male) from chart (e.g. .2/.5)
Probabilities written in the margins of table are called marginal probabilities
Independence (section 3.2)
definition of independence: P(A) = P(A|B)
Alternative definition: P(A and B) = P(A)P(B)
What we do intuitively
Note: height and sex are not independent in above example
last updated: $Date: 2006-04-05 17:38:25 -0400 (Wed, 05 Apr 2006) $