LML/23$ ArialQ.oP4'?3#oP$ArialQ.oP4'?3#oP$ ArialQ.oP4'?3#oP@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 033  33  33 833  33 ` ` ` ` 833 0 33 833 33 33 33 33 833 833 833 833 833 833 833 833 833 833 833 833 833 833 0 33 833 033 833 833 833 833 0"33 833 833 833 833 833 0 833 833 833 833 @ 833 833 833 833 833 833 833 833 833 833 833 833 833 833 833 833 833 @ 3 @ @0 @0 0 0 @(0 @  0 3djY!_]<  ?8xEMQ$  A   ?o      H`?bQ4V@EX,b PPH\ 6HeRd]/L!R|_G)v-Hdp),S6RiT*ʦȤ} t*;%gZmVe>"#p0|[Mb@W*bm &rY~×htZ<]Gme<^QkF@X .-N%t&j qz-FOoD -S~^٪` ȝ @>1@(;>8 :ɪ`l&|x~ ~CpA$`pà  h Y?& Mb@?  #  f g i2  -./g 0d ook at t graph o P(Ai). F the inill happen if# >j6$u<7~7[\ZLLLLLLLLL L L L L L LPSM230, Spring 1997 - Single Sector Bayesian Search, Prof. John C. TurnerFSee page B for instructions. See page C for the assignment. `aP(Ai)LIaP(D|Ai) adt, ` at  $ ? $ @ $ @ $@ $@ $@ $@ $ @ $"@ $$@ $&@ $(@ $*@ $,@ $.@ $0@ $1@ $2@ $3@ $4@ $5@ $ 6@ $!7@ $"8@ $#9@ $$:@ $%;@ $&<@ $'=@ $(>@ $)?@ $*@@ $+@@ $,A@ $-A@ $.B@ $/B@ $0C@ $1C@ $2D@ $3D@ $4E@ $5E@ $6F@ $7F@ $8G@ $9G@ $:H@ $;H@ $<I@ $=I@ $>J@ $?J@ $@K@ $AK@ $BL@ $CL@ $DM@ $EM@ $FN@ $GN@ $HO@ $IO@ $JP@ $K@P@ $LP@  aA1s?{433333? $433333?  aP(A1)? m?$ u?  $ uZZZZZZ?  $ uGXi?  $u$I$I?  $uHXi?  $uJ)RJ?  $uqڊ?  $u7?  $u2Avs?  $u 2?  $u2Avs?  $u ?  $uʼnxe?  $u3um?  $uY`X0?  $uӏ5?  $ufM?  $u14K?  $u)$ݫ?  $up u8mm]?  $?u\ ǡx?  $@uouE?  $Auk7}W?  $BuX&la]?  $Cu^I~?  $Du£K?  $Eu'J?  $FuƊ^?  $Gu/?Q?  $Hu?  $Iur?  $Jȗi?  $KuI 8?  $Lud. ?   aA2?? $?  aP(A2) ?$ u?  $ u?  $ u|a?  $uX?  $uE?  $un?  $ux7Ɉ?  $u= ?  $u"Iǟ?  $u$?  $uX|(?  $uYY?  $u+?  $u6Ht?  $uuވ!?  $?u/8?  $@ucv?  $AuAG?  $BuRP?  $Cu :?  $DuR|#6?  $EuH?  $Fu1L{?  $GuJٟP?  $Huȳo?  $Iup]E?  $Jul?  $KuҀ?  $LuD+)J?   aA3333333?433333? $433333?  aP(A3) 333333?$ u?  $ u;<<<<x?  $:ukD?  $;uu,ʔ ?  $?u(mpS?  $@u_VV?  $Au[|?  $BuO\?  $Cu/-O?  $Duj?  $EuDs?  $FuHc^?  $Gumy?  $Hu&CH?  $Iuv/c\?  $Ju?  $KuT^B?  $Lu"\?   aA4?? $?  aP(A4) ?$ u?  $ uҲ?  $ u|a?  $uX?  $uE?  $un?  $ux7Ɉ?  $u= ?  $uM?  $uU+n(p?  $u1ɖ?  $uGLG?  $u*#?  $u?  $u. 3ځ?  $u ;;E?  $u^8R4?  $u볶?  $uFdGr?  $u ?  $uE@"?  $ u_[?  $!uXǼә?  $"uxsW?  $#uV@?  $$u<ސ?  $%u-K?  $&ukU?  $'uZHū?  $(u5_|?  $)u7OC`[?  $*uVf?  $+uO,_/?  $,uYb?  $-uX?  $.ujp ?  $/u ?  $0u[ި?  $1uYĄm?  $2uJ %x?  $3u4H&?  $4uj[?  $5u;J:ӏ?  $6uۇ4?  $7uڊlg?  $8u`C1?  $9u3Q=?  $:uW<|z?  $;u^,q?  $<uO~,?  $=uB l7?  $>u1?  $?uA`پ?  $@u?  $Au&~?  $BuA?  $CuІڧ?  $DuaE?  $Eu9A?  $FuHn?  $GuM?  $HuKļ?  $IudNF?  $Ju߉?  $KuY &?  $Lu )?   aSUM"e?P ` ` `% Q? % 333333? % ? % _(ٵ? %__? %_(ٵ? %Z/Y? %螪 ? %:$C>μ? %'? %vZp3{? %'? %! 2s? %ҩRH ? %׿E? %P5P? % r? % (Y ? %A? %f+u=ξ? %8$?? %&R 02? %'lS؇.? %($c? %)a揱? %*;J? %+@>_? %,W[ڶU? %-o6? %.DJ3? %/ g*? %0gJ? %1\TI? %2V.޽? %3AM? %4>? %5>? %6E? %7NΡ .? %8_jǻ? %9aM? %:Ati? %;8$! ? %<~ ? %=ї G? %>!? %?ވ!? %?/8? %@cv? %AAG? %BRP? %C :? %DR|#6? %EH? %F1L{? %GJٟP? %Hȳo? %Ip]E? %Jl? %KҀ? %LD+)J?  `  `% ףp= ? % ̼? % ? % =? %Qβ? %wÏ? %,j5? %yRT? %\{y? %ptlA^`? %HL4? %I1xa? %ṅ\? %f/? %@Nū? %]hј? %؛4D? %'qrGR? %֥? %/w? % O7? %!A~? %"-fz? %#k-V? %$lxW? %%;]:d? %&;:f? %'? %(? %) W"ױ? %*b0? %+z+승? %,J3? %-z(N? %.4? %/T"1? %0?7? %1O>a? %2j qć? %3qQ? %4w13? %5s)˵? %6Ms-_? %7UӨd~.? %<fE? %=(4b? %>L&LP? %?MA2? %@ "}? %A; ɹ? %B ݽ? %CN8? %D+{ ? %E//ޅ#? %FW*? %GF_m? %H ? %I? %J3Q? %KfOdN? %Lң>Z?  `  `% |Gz? % ? % ? % {a? %:/? %kgJ8? %u:~? %?&ǒ::? %>d;3? %審? % ? %? % 9? %pUO? %GW? %]i? %w^|? %At? %lV^? %bil[? %Pқ? %o$4m? % 3? %!9{? %"ƚ F? %# $>? %$stQ? %%So? %&VDkU? %' 7? %("I`? %)Xf ? %*gM? %+u%,? %,?O$6? %-t ? %.Ul&=? %/AS:? %0v? %1 6j$? %2BDCo? %3lİ? %4ï? %5c;lB? %6 T? %7og? %8jύ? %9\ʡ? %:F0ܖ/? %;zV'? %<Jڗ? %=O5V, ? %>g? %?t)筸? %@[N$ؽ? %At|? %Bosn4? %C#8? %DjӦ? %E(ʜP? %FIX? %GrbHG? %H;? %I ? %J_t? %K(:l? %Lx?   ` aMax." U?T" 333333?T" ?T"  =?T" __?T" _(ٵ?T" n?T" 螪 ?T" >d;3?T" >yRT?T" vZp3{?T" X|(?T" ! 2s?T" I1xa?T" ׿E?T" _?T" ,W[ڶU?T" -Zm:W?T" .4?T" /AS:?T" 0gJ?T" 1\TI?T" 2)S?T" 3qQ?T" 4>?T" 5# ?T" 6E?T" 7NΡ .?T" 8jύ?T" 9?~?T" :K3?T" ;8$! ?T" <~ ?T" =\6I?T" >L&LP?T" ??,  ; H ;T>?4  ; @ < i Y?,  ; H < i Y?4  ; @ =a0!?,  ; H =a0!?4  ; @ >8mm]?,  ; H >8mm]?4  ; @ ?yHT?,  ; H ?yHT?4  ; @ @&(?,  ; H @&(?4  ; @ Ak7}W?,  ; H Ak7}W?4  ; @ BX&la]?,  ; H BX&la]?4  ; @ CP])}?,  ; H CP])}?4  ; @ D£K?,  ; H D£K?4  ; @ EЛ?,  ; H EЛ?4  ; @ FƊ^?,  ; H FƊ^?4  ; @ G{z??,  ; H G{z??4  ; @ H9C?,  ; H H9C?4  ; @ Ir?,  ; H Ir?4  ; @ J̑i?,  ; H J̑i?4  ; @ Khx+?,  ; H Khx+?4  ; @ Ld. ?,  ; H Ld. ?4  ; @ ?,  ; H ?4  ; @ ?,  ; H ?4  ; @ ?,  ; H ?4  ; @ |a?,  ; H |a?4  ; @ X?,  ; H X?4  ; @ E?,  ; H E?4  ; @ n?,  ; H n?4  ; @ x7Ɉ?,  ; H x7Ɉ?4  ; @ = ?,  ; H = ?4  ; @ "Iǟ?,  ; H "Iǟ?4  ; @ $?,  ; H $?4  ; @ X|(?,  ; H X|(?4  ; @ YY?,  ; H YY?4  ; @ +?,  ; H +?4  ; @ 6Ht?,  ; H 6Ht?4  ; @ ވ!?,  ; H >ވ!?4  ; @ ?/8?,  ; H ?/8?4  ; @ @cv?,  ; H @cv?4  ; @ AAG?,  ; H AAG?4  ; @ BRP?,  ; H BRP?4  ; @ C :?,  ; H C :?4  ; @ DR|#6?,  ; H DR|#6?4  ; @ EH?,  ; H EH?4  ; @ F1L{?,  ; H F1L{?4  ; @ GJٟP?,  ; H GJٟP?4  ; @ Hȳo?,  ; H Hȳo?4  ; @ Ip]E?,  ; H Ip]E?4  ; @ Jl?,  ; H Jl?4  ; @ KҀ?,  ; H KҀ?4  ; @ LD+)J?,  ; H LD+)J?4  ;  amodified P(Ai¬ D)@ 333333?,  ; H 333333?4  ; @ ?,  ; H ?4  ; @ ;<<<<xݺ?,  ; H >xݺ?4  ; @ ?(mpS?,  ; H ?(mpS?4  ; @ @_VV?,  ; H @_VV?4  ; @ A[|?,  ; H A[|?4  ; @ BO\?,  ; H BO\?4  ; @ C/-O?,  ; H C/-O?4  ; @ D{ D: ?,  ; H D{ D: ?4  ; @ EDs?,  ; H EDs?4  ; @ FHc^?,  ; H FHc^?4  ; @ Gmy?,  ; H Gmy?4  ; @ H&CH?,  ; H H&CH?4  ; @ Il-?,  ; H Il-?4  ; @ J?,  ; H J?4  ; @ KT^B?,  ; H KT^B?4  ; @ L"\?,  ; H L"\?4  ; @ ?,  ; H ?4  ; @ ?,  ; H ?4  ; @ Ҳ?,  ; H Ҳ?4  ; @ |a?,  ; H |a?4  ; @ X?,  ; H X?4  ; @ E?,  ; H E?4  ; @ n?,  ; H n?4  ; @ x7Ɉ?,  ; H x7Ɉ?4  ; @ <d;3?,  ; H <d;3?4  ; @ M?,  ; H M?4  ; @ U+n(p?,  ; H U+n(p?4  ; @ 1ɖ?,  ; H 1ɖ?4  ; @ GLG?,  ; H GLG?4  ; @ *#?,  ; H *#?4  ; @ ?,  ; H ?4  ; @ . 3ځ?,  ; H . 3ځ?4  ; @  ;;E?,  ; H  ;;E?4  ; @ At?,  ; H At?4  ; @ 볶?,  ; H 볶?4  ; @ FdGr?,  ; H FdGr?4  ; @  ?,  ; H  ?4  ; @ E@"?,  ; H E@"?4  ; @ _[?,  ; H _[?4  ; @ !XǼә?,  ; H !XǼә?4  ; @ "xsW?,  ; H "xsW?4  ; @ #V@?,  ; H #V@?4  ; @ $<ސ?,  ; H $<ސ?4  ; @ %So?,  ; H %So?4  ; @ &kU?,  ; H &kU?4  ; @ 'ZHū?,  ; H 'ZHū?4  ; @ (5_|?,  ; H (5_|?4  ; @ )7OC`[?,  ; H )7OC`[?4  ; @ *Vf?,  ; H *Vf?4  ; @ +O,_/?,  ; H +O,_/?4  ; @ ,Yb?,  ; H ,Yb?4  ; @ -X?,  ; H -X?4  ; @ .jp ?,  ; H .jp ?4  ; @ /?S:Ӥ?,  ; H /?S:Ӥ?4  ; @ 0[ި?,  ; H 0[ި?4  ; @ 1YĄm?,  ; H 1YĄm?4  ; @ 2J %x?,  ; H 2J %x?4  ; @ 34H&?,  ; H 34H&?4  ; @ 4j[?,  ; H 4j[?4  ; @ 5;J:ӏ?,  ; H 5;J:ӏ?4  ; @ 6ۇ4?,  ; H 6ۇ4?4  ; @ 7ڊlg?,  ; H 7ڊlg?4  ; @ 8hύ?,  ; H 8hύ?4  ; @ 93Q=?,  ; H 93Q=?4  ; @ :W<|z?,  ; H :W<|z?4  ; @ ;^,q?,  ; H ;^,q?4  ; @ <O~,?,  ; H <O~,?4  ; @ =B l7?,  ; H =B l7?4  ; @ >1?,  ; H >1?4  ; @ ?A`پ?,  ; H ?A`پ?4  ; @ @?,  ; H @?4  ; @ As|?,  ; H As|?4  ; @ BA?,  ; H BA?4  ; @ CІڧ?,  ; H CІڧ?4  ; @ DaE?,  ; H DaE?4  ; @ E9A?,  ; H E9A?4  ; @ FHn?,  ; H FHn?4  ; @ GM?,  ; H GM?4  ; @ HKļ?,  ; H HKļ?4  ; @ IdNF?,  ; H IdNF?4  ; @ J߉?,  ; H J߉?4  ; @ KY &?,  ; H KY &?4  ; @ Lw?,  ; H Lw?4  ;   SUM" ?P" 233333?P" KKKKKK?P" >?P"9:?P")ٵ]?P"Fd?P"FXw?P"p&13?P"Fa?P"b#s?P"?P"|3?P"?P" 9?P"Ъk?P"B =L#?P"o"[?P"/RQN?P"jfE?P"GVԓ?P"nۂ?P" ܲ\?P"!!?P""y?P"# Ԗt?P"$p%{?P"%$?P"&[|g?P"'e ^?P"(l+?P"?1u?P"@n.O?P"A^ՠ?P"BW+?P"C6r?P"D>5?P"Ej.?P"F !?P"G9j?P"H*`?P"I\ {?P"J$P?P"K6W/&"?P"LA?P$u<7~7[\6        Dgb3PSM230, Spring 1997 - Single Sector Bayesian Search, Prof. John C. TurnerInstructions:4Enter P(Ai) and P(D|Ai) in the cells in red.HBe sure the SUM of P(Ai) is 1. The sum of P(D|Ai) need not be 1.<aSet dt to the time increment. (Initially, use dt=1).lIn the rows t=0,1, 2, ... the gray columns are the (updated) probabilities of being in each sector,.given we have not yet found the pilot.Z The next 4 (blue) columns are the entries in the Venn diagram for Prob(Ai and D).\ aThe next column is the max of Prob(Ai and D). This tells us which sector to search.v aIn the next 4 (olive) columns, we use Prob(Ai)*Prob(D) if we search this sector, Prob(Ai) if we do not search.n The last column (labeled SUM in magenta) is the sum of the conditional probabilities, namely P(not D).f Check that in row 2, P(Ai)=P(Ai¬ D)/P(not D), where the values on the right hand side comefrom row 1.4To add more rows, highlight the bottom row.0a'(Be sure it's not the row labeled t=0.)Q:Then press Ctl-C or /Edit, Copy, or the Copy icon.DThen highlight one or more blank cells in the first column.:Then press Ctl-V or /Edit,Paste or the Paste Icon. `  `  ` `  `  ` `  `  ` `  `  ` `  `  ` `  `  ` `  `  ` `  `  `$u<7~7[\gb3PSM230, Spring 1997 - Single Sector Bayesian Search, Prof. John C. TurnerAssignment:B1. Look at the graph of P(Ai and D). Press F11 and Enter. .aThis tells us which sector to search.2With dt=1, what does this graph look like?T2. Change dt to 0.5 and then to 0.2 and 0.1. How does this affect the graph?N3. Where the top two curves cross (join) has a special interpretation.What is it?B Does the point of intersection change as dt gets smaller?F 4. How do you interpret the way the top two curves intertwine?: aThat is, what does this mean to the search team?@ 5. The bottom curve eventually rises to join the others. Why is it so slow?:What determines which curve will join first? Last?Ddd I_^[Group14Group1do 7N*?1&OM=*?1NSw=:  # # #4QPW$ExtendedStorage$6.0