UNR, MATH/STAT 352, Spring 2007. Time EruptionWaiting timeEruption.
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Transcript of UNR, MATH/STAT 352, Spring 2007. Time EruptionWaiting timeEruption.
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
TimeEruption Waiting time Eruption
UNR, MATH/STAT 352, Spring 2007
Long waitShort wait
UNR, MATH/STAT 352, Spring 2007
Long eruptionShort eruption
UNR, MATH/STAT 352, Spring 2007
Short eruption, short wait
Long eruption, long 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
http://www.worldviewofglobalwarming.org
Carbon DioxideCO2
Temperature
Carbon dioxide concentration is related to the Earth temperature
UNR, MATH/STAT 352, Spring 2007
http://www.seed.slb.com
Carbon dioxide concentration is related to the Earth temperature
UNR, MATH/STAT 352, Spring 2007
http://www.greendiary.com
Possible solution:Control CO2 to affect temperature
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) ?
http://www.e-stockpro.com
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 variablesb) establish connections among random variables
UNR, MATH/STAT 352, Spring 2007
Experiment: tossing two dice, face of each die isa random variable with possible values {1,2,3,4,5,6}
Sample space
(1,1)
(2,1)
(1,2)
(2,2)
(1,3)
(2,3)
(1,4)
(2,4)
(1,5)
(2,5)
(1,6)
(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(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)
Second die (2nd random variable)
Fir
st
die
(1
st ra
nd
om
vari
ab
le)
Each outcome (n,m)has probability
1/36
UNR, MATH/STAT 352, Spring 2007
Experiment: observing two random variables X and Y
Sample spaceRandom variable Y
Ran
dom
vari
ab
le X
Probabilities canbe calculated using
density f(x,y)