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;: 11‘" ti, ” lg» iii
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“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:
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. , ZPMMAIAA
” 7 .. . i=1 5}. it» ,1..
.1 5 5,31, T 51:55 (The: 5 ._ ,1 555% 5)»? L .i 5:}.
, where P(Aﬂ.Aj=PU1A)i3(A) to obtain ' “jix’
W. '\ f ,‘x 5 a. \
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l a 3—; 105443514) M :5; «9.. T f T 1‘13],
. .‘ . (ﬁrtrim ﬁx  1 555553? 3‘ ‘* —‘ '1
5 2 1 ‘~.? 5 ZPWHAJA» ~ 555.. 5 T TTT m
.. * 1 i=1 deg—ti lQ 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. 'mVL", . 4“ 5;. ;'* . ~!“"r ,.
’ 1;? .1} ‘33 5 T 7 .9; .q ...
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 Fall '07
 Carlton

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