I'm trying to obtain a sum distribution of two discrete random variables. The function TransformedDistribution doesn't work for me in such case:

Z = EmpiricalDistribution[{0.7, 0.3} -> {0, 1}] Y = EmpiricalDistribution[{0.6, 0.4} -> {0, 1}]

TransformedDistribution[z+y,{z [Distributed] Z, y [Distributed] Y}]

It gives an answer, which seems as a distribution of z+y, but when I ask to calculate a mean or CDF or PDF it gives no answer.

TransformedDistribution works well for named distributions - geometric, poisson and etc.

Thanks in advance.

I'm trying to obtain a sum distribution of two discrete random variables. The function TransformedDistribution doesn't work for me in such case:

Z = EmpiricalDistribution[{0.7, 0.3} -> {0, 1}];
Y = EmpiricalDistribution[{0.6, 0.4} -> {0, 1}];

TransformedDistribution[z+y,{z \[Distributed] Z, y \[Distributed] Y}]

It gives an answer, which seems as a distribution of z+y, but when I ask to calculate a mean or CDF or PDF it gives no answer.

TransformedDistribution works well for named distributions - geometric, poisson and etc.

Thanks in advance.