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Section 6.5 Generating Functions for Uniform-based Distributions

Moment Generating Functions 5.5.1 can be derived for each of the distributions in this chapter.
Presuming R = {1, 2, ..., n},
M(t)=βˆ‘x=1netx/n=1nβ‹…[et+e2t+...ent]
Presuming R = [a,b],
M(t)=∫abetx1bβˆ’adx=1bβˆ’a1tetx|ab=ebxβˆ’eaxbβˆ’a
M(t)=βˆ‘x=0n1etx(n1x)(nβˆ’n1rβˆ’x)(nr)=a mess...