Statistics 528  Lecture 14
1
Statistics 528  Lecture 14
Prof. Kate Calder
1
Probability
Statistical Inference
Question:
How often would this method give the correct answer if I used
it many times?
Answer:
Use laws of probability.
Statistics 528  Lecture 14
Prof. Kate Calder
2
Example:
Tossing a coin
If the coin is fair (chance of heads = chance of tails) then
•
1 toss  you don’t know whether you will get heads or tails
•
Many tosses  the proportion of tosses where you get heads is close to
50% (IPS Probability Applet)
=> The outcome is predictable, but only
in the long run
.
Statistics 528  Lecture 14
Prof. Kate Calder
3
Random:
We call a phenomena
random
if individual outcomes are
uncertain but there is a predictable pattern of outcomes in the long run.
Note: Random Haphazard
Probability:
The
probability
of any outcome of a random phenomena is
the proportion of times the outcome would occur in a large number of
repetitions.
(probability = longterm relative frequency)
≠
Statistics 528  Lecture 14
Prof. Kate Calder
4
Probability Models
•
Now let us try to model a random phenomenon.
•
For example, consider tossing a fair coin. We don’t know the outcome
in advance, but we can say the following:
Possible outcomes: Heads, Tails
Probability of each outcome: 0.5, 0.5
Statistics 528  Lecture 14
Prof. Kate Calder
5
•
A
probability model
consists of
1.
sample space (
S
)
– the set of all possible outcomes
2. probability for each outcome
•
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 Winter '09
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 ABO blood group system, Prof. Kate Calder

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