# Metropolis-Hastings algorithm

## Main Question or Discussion Point

I'm having trouble understanding how to find an expression for $$\pi(x)$$ and $$\pi(y)$$ in the relation:
$$\alpha \left( {x,y} \right) = \min \left( {1,\frac{{\pi \left( y \right)q\left( {y,x} \right)}}{{\pi \left( x \right)q\left( {x,y} \right)}}} \right)$$
For example, If I want to simulate Normal Distribution (Expectation value m and standard deviation s), how can I find expressions for $$\pi(x)$$ and $$\pi(y)$$? Or are they equal: $$\pi(x)=\pi(y)$$?