Question: Let X be a simple r.v. defined on (W, A ), so that Where { A j , j = 1,¦., n } is a

LetXbe a simple r.v. defined on (W,A), so that

a jIAj X-Σ-aA |X = j=1

Where {Aj, j = 1,€¦., n} is a (measurable) partition of W, and the aj, j = 1,€¦., n, are assumed to be distinct. Next, let

Let X be a simple r.v. defined on ((, A),

Be ay other representation of X. Then show that each Aj, j = 1,€¦., n is the sum of some Bi€™s.

a jIAj X--aA |X = j=1

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