Transcript Lecture 8

UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
Time
Eruption
Waiting time
UNR, MATH/STAT 352, Spring 2007
Eruption
Long wait
Short wait
UNR, MATH/STAT 352, Spring 2007
Long eruption
Short eruption
UNR, MATH/STAT 352, Spring 2007
Long eruption, long wait
Short eruption, short wait
UNR, MATH/STAT 352, Spring 2007
Conclusion:
The longer the eruption, the longer the wait
for the next one
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
Carbon dioxide concentration is related to the Earth temperature
Carbon Dioxide
CO2
Temperature
http://www.worldviewofglobalwarming.org
UNR, MATH/STAT 352, Spring 2007
Carbon dioxide concentration is related to the Earth temperature
http://www.seed.slb.com
UNR, MATH/STAT 352, Spring 2007
Possible solution:
Control CO2 to affect temperature
http://www.greendiary.com
UNR, MATH/STAT 352, Spring 2007
?
Each asset can be described by the (possible)
distribution of future values.
UNR, MATH/STAT 352, Spring 2007
Asset A
Asset B
Portfolio (A+B)
UNR, MATH/STAT 352, Spring 2007
Some processes (and random variables) are connected
We can measure (or control) one process to predict
(or control) another
Thus, we need to
a) manipulate with several random variables
b) establish connections among random variables
UNR, MATH/STAT 352, Spring 2007
Experiment: tossing two dice, face of each die is
a random variable with possible values {1,2,3,4,5,6}
First die (1st random variable)
Second die (2nd random variable)
Sample space
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
Each outcome (n,m)
has probability
1/36
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
UNR, MATH/STAT 352, Spring 2007
Experiment: observing two random variables X and Y
Sample space
Random variable X
Random variable Y
Probabilities can
be calculated using
density f(x,y)
UNR, MATH/STAT 352, Spring 2007