| 11. | Also, generating the generating function is very easy, you just iterate this process.
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| 12. | We say that the discrete random variable Y satisfying probability generating function characterization
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| 13. | "It's not just PCs-- cars now have more chip-generated functions ."
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| 14. | Probability generating functions obey all the rules of power series with non-negative coefficients.
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| 15. | All higher characteristic function and moment generating function are both equal to one.
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| 16. | More concretely, their generating functions are equal after an appropriate change of variables.
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| 17. | The generating function given above for is a special case of this formula.
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| 18. | This can be seen by comparing the generating function of the Hermite polynomials
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| 19. | We define that any discrete random variable Y satisfying probability generating function characterization
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| 20. | One of the most well-known of these, the generating function for Legendre polynomials,
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