Hi,

I’m looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables.

This would be easy if they were independent, but they’re not. There is a known correlation between the variables.

Question: how to combine two discrete random variables with correlation?

Given: The marginal probabilities of the two variables & a correlation function

Result: either the individual probabilities in a probability table or the complete probability distribution of the combination.

Simple example:

Variables A and B are the distributions:

PA(a=1, 4) = [0.75, 0.25]

PB(b=4, 8, 10) = [0.25, 0.25, 0.5]

Their joint probability function is shown in their joint probability table and joint value table:

P B=4 8 10

A=1 ? ? ? 0.75

4 ? ? ? 0.25

0.25 0.25 0.5 1

value B=4 8 10

A=1 4 8 10

4 16 32 40

(tables are clearer in attached file)

The correlation between the two variables is: b = 10 – 2/3*a

P(A*B)(4, 8, 10, 16, 32, 40) = ?

I’m looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables.

This would be easy if they were independent, but they’re not. There is a known correlation between the variables.

Question: how to combine two discrete random variables with correlation?

Given: The marginal probabilities of the two variables & a correlation function

Result: either the individual probabilities in a probability table or the complete probability distribution of the combination.

Simple example:

Variables A and B are the distributions:

PA(a=1, 4) = [0.75, 0.25]

PB(b=4, 8, 10) = [0.25, 0.25, 0.5]

Their joint probability function is shown in their joint probability table and joint value table:

P B=4 8 10

A=1 ? ? ? 0.75

4 ? ? ? 0.25

0.25 0.25 0.5 1

value B=4 8 10

A=1 4 8 10

4 16 32 40

(tables are clearer in attached file)

The correlation between the two variables is: b = 10 – 2/3*a

P(A*B)(4, 8, 10, 16, 32, 40) = ?

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