±
i
±²
Hint:
12
3
3
1
1
2
X
Xi
x
i
nn
n
n
n
ECE302 Homework #2
±
±±
²
²
²²
±
∩
∩ ∩³³³∩
 ³³³³³
 ∩³³³∩
+
1
( )= exp( )
1
5
13
15
5
()=
1
2
= 1012345
5
Pr(
) =Pr( )
Pr( ) Pr( )
)=Pr( )Pr(
)
)
kk
n
±
±
n
X
X
X
fx k
x
,
x .
k
X<
<X .
X<.
X.
X
p x k
, x
,,,,,,.
k.
A,B
C
AB C
A
S,²,A
S
²
A
AB
A
,
B
AA
A
A
A
A
A
A
A
Assigned 1/24/10, Due 2/5/10 (by 4:30 in dropbox in MSEE 330)
1. Text, problem 2.102, p. 91.
given that
errors have occured in operations,
each error can be further broken down according to a Bernouilli trial, with probability that
it is type 1, and probability
that it is type
2. Anabsentmindedprofessor has keysinhispocketof whichonlyone (hedoesnot remember
which one) ±ts his oﬃce door. He picks a key at random and tries it on his door. If that does
not work, he picks a key again to try, and so on until the door unlocks. Let
denote the
number of keys that he tries. Find the pmf of in the following two cases:
(a) A key that does not work is put back in his pocket so that when he picks another key,
all n keys are equally likely to be picked (sampling with replacement).
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 Spring '08
 GELFAND
 Discrete probability distribution, cdf FX

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