LM/23$ Arial7OY<#3;Y$Arial7OY<#3;Y$ Arial7OY<#3;Y@TMonth' 'D', 'YYYY Normal Comma Currency Percent Fixed DateHeading 1Heading 2 Total Comma0 Currency0 033 R033 2033 B033 033 x033 033 033 0 33 P033 0033 833 033 833 833 833 033 833 833 833 `33 `33 `33 `33 33 33  33  33  33  33 833 833 833 833 833 @ 33 @33 @33 @33 @(33 @33djY!_]<  ?C'OQ$  A   ?a      H`?bQ4V@EX,b PPH\ 6HeRd]/L!R|_G)v-Hdp),S6RiT*ʦȤ} t*;%gZmVe>"+ nW,ky_5!$QASL 'Na7aHpVhj]σk； pUy>V`Z$@}[h@V vTy @?Μ@>t(G3"ɨ@L*$|xɟ~~Dq( B ,x|H?1Rk[ڋ@Q J0r fQtv&B$jh#%,0 |9S: oY?& Mb@?  #  f g i2  -./g 0d tPWV W~ dž4 hjtPuK u3_^[6$u<7~7[\      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~HSM230, Fall 1996 - Simple Bayesian Search, Prof. John C. Turner~DSee page B for instructions. See page C for the assignment. P(Ai)P(D|Ai) t  @   @   @   @   @   @    @   "@   $@   &@   (@   *@   ,@   .@   0@   1@   2@   3@   4@   5@   6@   7@   8@   A1#?+433333?P(A1)??$ KyJ?  $ 8Moz?  $ )ULC?  $ H*?  $ {WEw?  $D?  $](6o?  $<?  $ s?  $"?  $ &a4?  $0-9jn?  $'?  $u${Ƚ?  $?  $^OL*?  $V?  $A#P?  $PW=?  $B9-?  $Ye?  $1 j?  $Al?   A23?;?P(A2)?$ G]tE?  $ 2?  $ Lfǀ(:?  $ J?  $ z^?  $l?  $J?  $=_.?  $U{?  $#?  ${?  $qV?  $Hy?  $y-qC?  $)(z?  $Dr?  $eC/j?  $w2%c?  $o^[?  $S?  $ klRK?  $2C?  $5j  $\x>  $ڳ>  $=Mǥ>  $/آ>  $NJ>  $WgK+>   A4C?K?P(A4)?$ )A?  $ q py?  $ ^۝`?  $ yYzmD?  $ <Ӝ4)?  $,[a?  $IP {>  $ÅH1̷>  $ 0R>  $}Z>  $D:>  $螢c>  $ }hF>  $)>  $s >  $G}=  $:ڮK=  $|lA=  $$y'L>=  $tQ |=  $0u`=  $6UB=  $ߥ%=   SUM"?P )Q?   ) ϖl?   ) 9E?   ) N+?   ) ejiC7?   ) o#?   )} ?   ) R?   )ٯ?   )HP?   )/±S?   )?   )}?   )X?   )Rf?k2?   )` VKA?   )hK?   )<z?S?   )zbX?   )\?   )^_?   ).-}a?   )U:Jb?   )Gc?   P(Ai¬ D))?   ) G]tE?   ) 2?   ) Lfǀ(:?   ) J?   ) z^?   )l?   )J?   )=_.?   )U{?   )#?   ){?   )qV?   )Hyy?   )y-qCr?   ))(j?   )Db?   )eC/Z?   )w2%S?   )o^K?   )C?   ) klR;?   )23?   )5j,?    )Q?   ) UxeW?   ) Qݨ)y?   ) <7l.?   ) M`,?   ) FUh>~?   )6Рr?   )VX`>-f?   )MmZ?   )ZbN?   )<~A?   )E|U4?   )})Yh'?   )2iU?   )?   )J?   )∉;>   )yS'>   )N|>   )J>   )x=lQ>   )F̳>   )g?>   )ؓޙ>    )zGz?   ) m?   ) pPZT?   ) =,:?   ) `W ?   ) /)?   )&>   )u>   )5Ӎ_>   )mxA>   )5Y{w>   ):]8[>   )d75?>   )!F1!>   )oo>   )#׏=   )Ђ b=   )+~߮=   )+=   )-1t=   )u :W=   )f:=   )5#uU-=   )??=    SUM" ?P" + ?P" f?P" a5> G?P" Ȃx?P" QJ.;?P" 0E?P" 7(& ?P" "m ?P" ;?P" ǵk,?P" 3yG =?P" H?P" cQ?P" ̱mW?P" /[?P" 7-$^?P" `?P" BA:b?P" O^c?P" csnd?P" d?P" :ee?P" .e?P                             ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                                                                                                                                 $u<7~7[\RY3HSM230, Fall 1996 - Simple Bayesian Search, Prof. John C. TurnerInstructions:4Enter P(Ai) and P(D|Ai) in the cells in red.HBe sure the SUM of P(Ai) is 1. The sum of P(D|Ai) need not be 1.jIn the rows t=1, 2, ... the gray columns are the (updated) probabilities of being in each sector,.given we have not yet found the pilot.TThe blue columns are the entries in the Venn diagram for Prob(Ai and not D).p The last column (labeled SUM in magenta) is the sum of the conditional probabilities, namely P(not D).f Check that in row 2, P(Ai)=P(Ai¬ D)/P(not D), where the values on the right hand side come from row 1.4 To add more rows, highlight the bottom row.0i'(Be sure it's not the row labeled t=1.)Q:Then press Ctl-C or /Edit, Copy, or the Copy icon.DThen highlight one or more blank cells in the first column.:Then press Ctl-V or /Edit,Paste or the Paste Icon.$u<7~7[\$Y3HSM230, Fall 1996 - Simple Bayesian Search, Prof. John C. TurnerAssignment:<1. Look at the graph of P(Ai). Press F11 and Enter. HiFor the initial values of P(Ai) and P(D|Ai), what will happen if<we search for a long time without finding the pilot?V2. What happens if you use the same values of P(D|Ai), but in different cells?0E.g., let P(D|A1)=0.50 and P(D|A2)=0.30.0You should notice two types of changes.L i'3. How does the graph change if you halve all the values of P(D|Ai)?> 4. Is it always true that only one graph climbs to 1?B Find a combination of (new) values for P(D|Ai) that cause two curves to grow. J 5. When two curves grow, they generally grow to different values.HWhat affects these values? Find P(D|A3) and P(D|A4) so that they"grow to the same value.add   Group14Group1do 7OQ*?1&OM=*?1OQBw=:  ; ; ;4QPW$ExtendedStorage$6.0