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#ú \ _ > E /) í b O ì _ \ v ^ 8 #Ý ¥ « º Q x û b2(5 7Â0 b Q v0b3¸ r 5 /% µ6õ l b s8j @0i M ²0 @ 6 ~ r M Y ·#Ø 2 w _ > 8 Z c 2(5 1*4)# C @ , A)F A, ò 6 G \ w E Z \ Æ ¥ b 2( b ²% ^ 2( ' *ü _ v , o A c9× Í j N&ã K K 8 v # C @)E)F K r K S G b ^# C W _ > 8 Z v. W Ê v)m ô § Ï î º ¿ µ º á î ¡>&)m § Ï>' Title Microsoft Word 1211ï¼¨ï¼°æ ²è¼ ç ¨ä¾ é ¼å ã «ã ç¢ºèª ã ã ã ã docx. Conditional expectations such as EXjY = 2 or EXjY = 5 are numbers If we consider EXjY = y, it is a number that depends on y So it is a function of y In this section we will study a new object EXjY that is a random variable We start with an example Example Roll a die until we get a 6 Let Y be the total number of rolls and X the.

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A e B N i p Ó A e B { E A ÃE X ^ j A m A N X ^ K X A V o v g Ȃǂ̃e u E F A B A e B N G ݁i J g G ݁A u L ʁA X e V i A ( J M) A z A r A g N. L E J b v 1/ Ƒ E F B/ l ̃C X g HOME f CONTENTS ( C X g ͑S jpg 摜) ̉摜 E C h E Y ̏ꍇ E N b N ŕۑ A } b N ̏ꍇ N b N ŕۑ ĉ B. ® ï Ð V t H j c X g ¼ ú { c Æ ² X Ø @ ¾ ê l § å ã { å ã s ì æ ¼ T P P P O æ O r S e TEL FAX · s Æ ± æ µ Ç Ò F ã R @ T Ê ² · s à e Ä à.

傫 ȃT C Y iE J b v ȏ j ̕ p ̃X g b v X u B J b v ɓ { ƁA n ƃR V ̂ J b v ł A { ̂ o X g Ǝx Ă ܂ BQB1510 ɔ ׂĉ J b v ̃{ ̑f ނƈʒu ς A X b L Ƃ V G b g ɂȂ ܂ B. W S G b Û4 #Õ ì æ b) 9 @>*'¹* ) %Ê'2 b4( _2n } O G \ _ ^ W S 6× º>*) b%Ê'2 / W Z 8 \>* I R) @ ò A ^ b 6 \ \ a } G \ @ ¨ 8 7 >* @ *ñ 6 W S G \ v ¾ 8 K Z>* _ c) c L u \ M. If a and b are constants, then E(aXb) = aE(X) b Proof E(aXb) = sum (ax kb) p(x k) = a sum{x kp(x k)} b sum{p(x k)} = aE(X) b Variance We often seek to summarize the essential properties of a random variable in as simple terms as possible The mean is one such property Let X = 0 with probability 1.

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