I want to calculate the p.d.f of two discrete random variables. However, when I made a toy example that random variable was `dist`

and I wanted to find p.d.f. of `dist+dist`

, it failed.

```
dist = EmpiricalDistribution({2/9, 5/9, 2/9} -> {-1, 0, 1});
ya(t_) := PDF(TransformedDistribution(2*x, {x (Distributed) dist}), t);
ya /@ Range(-10, 10)
(*Output: {0, 0, 0, 0, 0, 0, 0, 0, 2/9, 0, 5/9, 0, 2/9, 0, 0, 0, 0, 0, 0, 0, 0} *)
```

The output seems wrong, because the p.d.f. of the sum of two random variables should be the convolution of these two. Hence the correct answer should be

Where did I make a mistake?