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## Main Question or Discussion Point

I'm having trouble understanding how to find an expression for [tex]\pi(x)[/tex] and [tex]\pi(y)[/tex] in the relation:

[tex]

\alpha \left( {x,y} \right) = \min \left( {1,\frac{{\pi \left( y \right)q\left( {y,x} \right)}}{{\pi \left( x \right)q\left( {x,y} \right)}}} \right)

[/tex]

For example, If I want to simulate Normal Distribution (Expectation value

[tex]

\alpha \left( {x,y} \right) = \min \left( {1,\frac{{\pi \left( y \right)q\left( {y,x} \right)}}{{\pi \left( x \right)q\left( {x,y} \right)}}} \right)

[/tex]

For example, If I want to simulate Normal Distribution (Expectation value

*m*and standard deviation*s*), how can I find expressions for [tex]\pi(x)[/tex] and [tex]\pi(y)[/tex]? Or are they equal: [tex]\pi(x)=\pi(y)[/tex]?