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UNR, MATH/STAT 352, Spring 2007

Probability and Statistics. MATH/STAT 352. Spring 2007. Lecture 7: Several Random Variables Jointly Distributed Random Variables. (slides only contain intro). UNR, MATH/STAT 352, Spring 2007. Old Faithful Geither. UNR, MATH/STAT 352, Spring 2007. Old Faithful Geither. Time. Eruption.

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UNR, MATH/STAT 352, Spring 2007

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  1. Probability and Statistics MATH/STAT 352 Spring 2007 Lecture 7: Several Random Variables Jointly Distributed Random Variables (slides only contain intro) UNR, MATH/STAT 352, Spring 2007

  2. Old Faithful Geither UNR, MATH/STAT 352, Spring 2007

  3. Old Faithful Geither Time Eruption Waiting time Eruption UNR, MATH/STAT 352, Spring 2007

  4. Old Faithful Geither Long wait Short wait UNR, MATH/STAT 352, Spring 2007

  5. Old Faithful Geither Long eruption Short eruption UNR, MATH/STAT 352, Spring 2007

  6. Old Faithful Geither Long eruption, long wait Short eruption, short wait UNR, MATH/STAT 352, Spring 2007

  7. Old Faithful Geither Conclusion: The longer the eruption, the longer the wait for the next one UNR, MATH/STAT 352, Spring 2007

  8. Global Warming UNR, MATH/STAT 352, Spring 2007

  9. Global Warming Carbon dioxide concentration is related to the Earth temperature Carbon Dioxide CO2 Temperature http://www.worldviewofglobalwarming.org UNR, MATH/STAT 352, Spring 2007

  10. Global Warming Carbon dioxide concentration is related to the Earth temperature http://www.seed.slb.com UNR, MATH/STAT 352, Spring 2007

  11. Global Warming Possible solution: Control CO2 to affect temperature http://www.greendiary.com UNR, MATH/STAT 352, Spring 2007

  12. Portfolio management ? Each asset can be described by the (possible) distribution of future values. UNR, MATH/STAT 352, Spring 2007

  13. Portfolio management Asset A Asset B http://www.e-stockpro.com Portfolio (A+B) ? UNR, MATH/STAT 352, Spring 2007

  14. 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

  15. Joint Distribution Experiment: tossing two dice, face of each die is a random variable with possible values {1,2,3,4,5,6} 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) Each outcome (n,m) has probability 1/36 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) First die (1st random variable) (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

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

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