It is well-known that a sum of normal r.v.'s is another normal r.v., and a sum of log-normal r.v.'s can be accurately approximated with a log-normal r.v. But what can we say if we have a mixture of both types is the sum? Is there any other approximation?
The second question is regarding the product. Again, it is not a secret that a product of log-normal r.v.'s is another log-normal r.v., and a product of normal r.v.'s is already not that straight-forward. But can one draw any conclusion regardig the product of normal and log-normal r.v.'s?