Memo # 1964-2 PDF - Verio

(5.7)
& c l
• • •
,
E,e k
9
the sum of which is the probability
(€ 1 1- *** +e k )
(5.8) Rte. = 110 - -240
r = 2 may be obtained in ( k ) different ways, namely by taking any
two of the.'s a l to be 1, the rest of them being o. The probabilities
of these combinations are
,2„ ,2„ ,2„ 2
k
(5.9)
(-- - 1'2 (- '1'3 (- '2'3
ck-1
--TTTr
'
r
'(0 ' r '( ) ' "" 240
and the suni of them is
(5.1o)
1:qa =210 -
2( 1 c 2 1- *** -1.ek-lk )
r(0
In general a .
= r may be obtained in ( k r
) different ways, namely
bytakinganyroutofthek. a l 's to be 1, the rest of them being
o. The probabilities of these combinations being
(5.11)
* 6 1'" c r-l cri-1
)
• • •
r
's-
k-r+1'" c k
(E)
the probability of a = r becomes
(5.12) pfa . =r10 - ,(0
where for short
(5.13)
7; = cl—Y-- +ck–r+i— cit •
In particUlar for r = k (5.13) has only one term
(5,14) = clE2wck •
If in (5.12) we let r pass through the values o,1,...,k all
possibilities have been ezaueted and therefore the probabilities
must add up to unity:
k
(5.15) Z p{a = rl = 1.
r=o