Addition and multiplication nodes can be used e.g. for constructing
linear mappings and affine transformations between the variables.
Denoting the inputs by , the outputs are
for
addition and
for multiplication nodes. The mean,
variance and expected exponential of the addition node are

(3) | |||

(4) | |||

(5) |

assuming independent. For a multiplication node, the expected exponential cannot be evaluated without knowing the exact distribution of the inputs. Assuming independence between , the mean and the variance of the output are

(6) | |||

(7) | |||

The equations for larger sums or products are obtained by induction, e.g. .