if we finding moment generating function then why we find incomplete moment generating function, weighted moment generating function in probability distribution

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 21E
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if we finding moment generating function then why we find incomplete moment generating function, weighted moment generating function in probability distribution?

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