| 11. | We define that any discrete random variable Y satisfying probability generating function characterization
|
| 12. | The generating function of the coefficients a _ n is then
|
| 13. | The result is that all generating functions involved have the form
|
| 14. | All higher characteristic function and moment generating function are both equal to one.
|
| 15. | In consequence the moment generating function is not defined.
|
| 16. | Similar asymptotic analysis is possible for exponential generating functions.
|
| 17. | The generating function given above for is a special case of this formula.
|
| 18. | So, let's try to find the solution using generating functions.
|
| 19. | It can be characterized by its moment generating function:
|
| 20. | The Cauchy distribution has no moment generating function.
|
