Calculate expected value of custom pdf

Question

I've a custom pdf in the sense that it's the convolution of several other PDFs

p[t_] := Convolve[p1[x],p2[x],x,t];

Now I want to calculate the expected value of this 'new' pdf w.r.t $t$

$\mu = \mathbb{E}_t [ p(t) ]$

How can I do this with mathematica?

Answer 1

Something like the following:

dist = ProbabilityDistribution[
  Convolve[PDF[NormalDistribution[4, 5], x], 
   PDF[NormalDistribution[3, 1], x], x, t], {t, -Infinity, Infinity}]

Expectation[z, z \[Distributed] dist]

(* 7 *)