Given a continuous uniform distribution over $[0,1]$, the MGF is $$\frac{e^t-1}{t} $$. How come it's "allowed" to generate say the 1st moment by using a Taylor expansion? Why can the discontinuity (at $t=0$) be fixed?
Thanks!
2026-03-30 05:13:47.1774847627
Calculating moments of a uniform distribution variable by fixing discontinuity of MGF.
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