Question

Probability distribution of difference of 2 normal distribution

Answer 1

have two probability density functions of normal distributions:

f1(x1|μ1,σ1)=1σ12π−−√e−(x−μ1)22σ21f1(x1|μ1,σ1)=1σ12πe−(x−μ1)22σ12

and

f2(x2|μ2,σ2)=1σ22π−−√e−(x−μ2)22σ22f2(x2|μ2,σ2)=1σ22πe−(x−μ2)22σ22

I'm looking for the probability density function of the separation between x1x1 and x2x2. I think that means I'm looking for the probability density function of |x1−x2||x1−x2|.