Pg 14 - P611215 fie T03 migrate/l “ 1(a\Vhst 1:3 the...

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Unformatted text preview: P611215 fie): T03 migrate/l “- 1/ (a) \Vhst 1:3 the probability the an error will occur in the tisansmissiun? if A. 1137:5553r ”Z" 3;: 1-1‘" ti, ” lg» iii WP) PCRPHSTD7LWR“ wnsr ) “Wentmnw+imlamfl59g (b) What IS the pruhabilitv that a 1 will be received? g “‘— any ravtmwew'nltflflifl .._. .55l5ifl «3) +537 ‘ 351393575; L.- 0 Suppose We are in the opposite situation. The event A has been observed, but it ie not know which {if the AT events have accurred. We can use. the definition of conditional probability in combination with the law of total probability to obtain the conditional probability of A; given A HAT; H A} ’ Pm) HAT N A) ll ll 3: 5313 2$3 "wit; :3”, 9%.. ”‘1,“ Kb!) :35; k . , ZPMMAIAA ” 7- .. . i=1 5}. it» ,1..- .1 5 5,31, T 51:55 (The: 5 ._ ,1 555% 5)»? L .i 5:}. , where P(A-fl.Aj=PU1A)i3(A) to obtain ' “-jix’ W. '\ f ,‘x 5 a. \ Mica £113.14» fin} PAAPA: :13 r” l a 3—; 105443514) M :5; «9-.-. T f T 1‘13], . .‘ . (fir-trim fix -- 1 555-553? 3‘ ‘* —‘ '1 5- 2 1 -‘-~.-? 5 ZPWHAJA» ~ 555.. 5 T TTT m .. * 1 i=1 deg—ti l-Q F” ii! in}: l' E) which is called Bag/65’ Formula or Bayes’ Rule 0 Example: The transmission uf hits over a binary communication channel has the fol— lowing characteristics: 0’s and 1 s have an equal chance of being sent. There is a 95% chance that a. sent 0 will be received .as 0. There is a 90% chance that a sent 1 will be received 3:51 "‘ ‘. E‘- 1- hr )‘\ .’ x; I" (a) Given a received 1 What is the probability uf 23. sent 1'? -’ , ,‘ 5. 1, V i" r‘- fill ” ’_ 2:57! 9 5~ 3 ' '5’. .T “Y. 'm-VL", . 4“ 5;. ;'* . -~!“"r- ,. ’ 1;? .1} ‘33 5 T -7 .9; .q ...
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