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

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UNR, MATH/STAT 352, Spring 2007

Time EruptionWaiting timeEruption

UNR, MATH/STAT 352, Spring 2007 Long wait Short wait

UNR, MATH/STAT 352, Spring 2007 Long eruption Short 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

Carbon Dioxide CO 2 Temperature Carbon dioxide concentration is related to the Earth temperature

UNR, MATH/STAT 352, Spring Carbon dioxide concentration is related to the Earth temperature

UNR, MATH/STAT 352, Spring Possible solution: Control CO 2 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) ?

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} 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 (2 nd random variable) First die (1 st random variable) Each outcome (n,m) has probability 1/36

UNR, MATH/STAT 352, Spring 2007 Experiment: observing two random variables X and Y Sample space Random variable Y Random variable X Probabilities can be calculated using density f ( x,y )