Applied Statistics
•
Probability
–
Probability of simple events
–
Probability of compound events
–
Probability using tree diagrams
–
Bayes Theorem
•
Probability Distribution
–
Probability pattern of discrete variables
–
Probability of continuous variables
–
Mean and mode of continuous variables
–
Binomial Distribution
–
Poisson Distribution
•
Regression
–
Regression lines and their equations

Probability, Set Operations
•
What is probability?
–
a branch of mathematical framework for reasoning about uncertainty
•
Classical Interpretation
: all outcomes have equal probability
–
dice {1,2,3,4,5,6}
P(1) =
1
/
6
,
P(2) =
1
/
6 …
•
Relative Frequency
–
P(pin-UP) = 32
–
P(pin-Down) = 68
•
Subjective Interpretation
(nature of problem): uses a model, randomness involved
–
such as weather
–
drop of paint falls into a glass of water, model can describe
P(hit bottom before sides
),
–
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 at basket.

Probability for Equally
Likely Outcomes

UK lottery ball frequency
UK lottery ball frequency
0
20
40
60
80
100
120
140
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49

500
1000
1500
2000
2500
3000
3500
4000
Heads
Tails
Counter intuity #1
Counter intuity #1
4000 flips of a Euro coin
4000 flips of a Euro coin
lands on “heads” 2780 times (68%)
lands on “heads” 2780 times (68%)
evidence of an unfair coin?
evidence of an unfair coin?

Calculating Probabilities
Calculating Probabilities
Minesweeper
Minesweeper
clicking on a cell containing a mine
clicking on a cell containing a mine
ends the game
ends the game
clicking on a cell containing no mine,
clicking on a cell containing no mine,
but adjacent to
but adjacent to
x
x
mines,will reveal the
mines,will reveal the
number of conjoining mines
number of conjoining mines
clicking on a square containing no mine,
clicking on a square containing no mine,
and not adjacent to a mine, will reveal nothing
and not adjacent to a mine, will reveal nothing

What is the probability of our first move
clicking on a cell containing a mine?
64 cells
10 mines
10 / 64 = 0.15625
15.6%
or
p = 0.156
What is the probability of clicking on a mine
in the highlighted block?
8 cells
1 mine
1 / 8 =
0.125
12.5%
or
p = 0.12
What about the green block
?
8 cells
3 mines
3 / 8 = 0.375
p = 0.375
Calculating Probabilities
Calculating Probabilities

Roulette
You plan to bet on number 13 on the next spin
of a roulette wheel.
What is the probability that you will
lose?
Solution
A roulette wheel has 38 different slots, only
one of which is the number 13.
A roulette wheel is
designed so that the 38 slots are equally likely.
Among
these 38 slots, there are 37 that result in a loss.
Because the sample space includes equally likely
outcomes, we use the classical approach (Rule 2) to get
P
(loss) =
37
38

Lecture Goals
•
Probabilistic models
–
Sample space
•
Which is basically a description of all the things that
may happen during a random experiment.

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- Summer '14
- PeterTino