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(OCR text)

Inversion theorem(5tl EIH)

On this subject, there is the following fundamental result. It is intimately

related to the inversion properties of Laplace transforms. Its proof requires so-

phisticated analytical machinery and is omitted.

Theorem 1. Inversion theorem

(a) Suppose that Mx (s) is finite for all s in an interval of the form -a, a],

where a is a positive number. Then, Mx determines uniquely the CDF of

the random variable X.

(b) If Mx (s) My (s)

< 00, for all s e-a, a], where a is a positive number,

then the random variables X and Y have the same CDF

omitL

!

Its proof is omitted...

MIT (2008)

13年11月8日金曜日

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