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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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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

Waiting time

Eruption

UNR, MATH/STAT 352, Spring 2007


Old Faithful Geither

Long wait

Short wait

UNR, MATH/STAT 352, Spring 2007


Old Faithful Geither

Long eruption

Short eruption

UNR, MATH/STAT 352, Spring 2007


Old Faithful Geither

Long eruption, long wait

Short eruption, short wait

UNR, MATH/STAT 352, Spring 2007


Old Faithful Geither

Conclusion:

The longer the eruption, the longer the wait

for the next one

UNR, MATH/STAT 352, Spring 2007


Global Warming

UNR, MATH/STAT 352, Spring 2007


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


Global Warming

Carbon dioxide concentration is related to the Earth temperature

http://www.seed.slb.com

UNR, MATH/STAT 352, Spring 2007


Global Warming

Possible solution:

Control CO2 to affect temperature

http://www.greendiary.com

UNR, MATH/STAT 352, Spring 2007


Portfolio management

?

Each asset can be described by the (possible)

distribution of future values.

UNR, MATH/STAT 352, Spring 2007


Portfolio management

Asset A

Asset B

http://www.e-stockpro.com

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


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


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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