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EE(g(X)jY)=E(g(X)) Proof Set Z = g(X) Statement (i) of Theorem 1 applies to any two rv’s Hence, applying it to Z and Y we obtain EE(ZjY)= E(Z) which is the same as EE(g(X)jY)= E(g(X)) 2 This property may seem to be more general statement than (i) in Theorem 1 The proof above shows that in fact these are equivalent statements 3. 1 Given g(x) = 3 x 1 (a) Evaluate and simplify completely i g( i2) ii g(0) iii g(1) iv g(4) v g(x 3) (b) Solve algebraically for x g(x) = 5 ii (x 2) = 4 iii g(x) 2 = 4 2 Simplify the di erence quotient f(x h) f(x) h for the following functions (a) f(x) = x2 2x 3 (b) f(x) = x3 5 (c) f(x) = 4 x 3 Simplify the following. LEXUS i N T X jTOYOTA i g ^ j 𒆐S ɂ G A p c u h B A e B V X s b c ARTISAN SPIRITS ƃC ^ A ̖ z C t @ N g OZ Racing Ƃ̃R { V ɂ Ēa Superturismo Evoluzione ̓ ʂȃR { V f ̓g h ̍Ő Z ^ b N X ^ C J o i T C Y Y J ԗ ^ Q b g ɊJ ܂ B @ ׂȃf U C { ꂽ X N ƃX c ւ̏ M ̌ 郌 b h S ƃT N ܂ l ̃J X ^ } C Y ̒ Ă e C X g ӂ 邱 ̃z C 甭 M Ă ܂ B.

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