18.05
Spring
2005
Lecture
Notes
18.05
Lecture
1
February
2,
2005
Required
Textbook
- DeGroot
Schervish,
“Probability
and
Statistics,”
Third
Edition
Recommended
Introduction
to
Probability
Text
- Feller,
Vol.
1
§
1.2-1.4.
Probability,
Set
Operations.
What
is
probability?
•
Classical
Interpretation:
all
outcomes
have
equal
probability
(coin,
dice)
•
Subjective
Interpretation
(nature
of
problem):
uses
a
model,
randomness
involved
(such
as
weather)
–
ex.
drop
of
paint
falls
into
a
glass
of
water,
model
can
describe
P
(hit
bottom
before
sides)
–
or,
P
(survival
after
surgery)- “subjective,”
estimated
by
the
doctor.
•
Frequency
Interpretation:
probability
based
on
history
–
P
(make
a
free
shot)
is
based
on
history
of
shots
made.
Experiment
↔
has
a
random
outcome.
1.
Sample
Space
- set
of
all
possible
outcomes.
coin:
S=
{
H,
T
}
,
die:
S=
{
1,
2,
3,
4,
5,
6
}
two
dice:
S=
{
(i,
j),
i,
j=1,
2,
...,
6
}
2.
Events
- any
subset
of
sample
space
ex.
A
√
S,
A
- collection
of
all