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MATH/STAT 352

Spring 2007

Lecture 7:

Several Random Variables

Jointly Distributed Random Variables

(slides only contain intro)

UNR, MATH/STAT 352, Spring 2007

UNR, MATH/STAT 352, Spring 2007

Long eruption, long wait

Short eruption, short 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

Carbon dioxide concentration is related to the Earth temperature

Carbon Dioxide

CO2

Temperature

http://www.worldviewofglobalwarming.org

UNR, MATH/STAT 352, Spring 2007

Carbon dioxide concentration is related to the Earth temperature

http://www.seed.slb.com

UNR, MATH/STAT 352, Spring 2007

Possible solution:

Control CO2 to affect temperature

http://www.greendiary.com

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

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

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

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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