relationship between two normally distributed variables

Question

Say I have two normally distributed independent random variables (X1 and X2) with the same variance but different means. How would I calculate P(X1 > X2)?

Answer 1

This is the same as $P \left(X_1-X_2>0\right)=\int_0^{\infty } \left(f_1\left( x\right)-f_2\left( x\right)\right) \, dx$

$$ =\frac{1}{2} \left(\frac{\text{erf} \text{$\mu $2}}{\sqrt{2} \sigma }-\frac{\text{erf} \text{$\mu $1}}{\sqrt{2} \sigma }\right)$$