UNR, MATH/STAT 352, Spring 2007. Time EruptionWaiting timeEruption.

UNR, MATH/STAT 352, Spring 2007


TimeEruption Waiting time Eruption


Long waitShort wait


Long eruptionShort eruption


Short eruption, short wait

Long eruption, long wait


Conclusion:The longer the eruption, the longer the wait for the next one


http://www.worldviewofglobalwarming.org

Carbon DioxideCO2

Temperature

Carbon dioxide concentration is related to the Earth temperature


http://www.seed.slb.com

Carbon dioxide concentration is related to the Earth temperature


http://www.greendiary.com

Possible solution:Control CO2 to affect temperature


?

Each asset can be described by the (possible) distribution of future values.


Asset A

Asset B

Portfolio (A+B) ?

http://www.e-stockpro.com


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


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


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)

UNR, MATH/STAT 352, Spring 2007. Time EruptionWaiting timeEruption.

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