ELEC210 Spring 2011 Homework3
1.
Let
ܺ
be the maximum of the number of heads obtained when Carlos and Michael each flip a
fair coin twice.
a)
Describe the underlying space
ܵ
of this random experiment and specify the
probabilities of its elementary events.
b)
Show the mapping from
ܵ
to
ܵ
, the range of
ܺ
.
c)
Find the probabilities for the various values of
ܺ
.
d)
Compare the pmf of
ܺ
with the pmf of
ܻ
, the number of heads in two tosses of a fair
coin. Explain the difference.
e)
Suppose that Carlos uses a coin with probabilities of heads
= 3/4
. Find the pmf of
ܺ
.
2.
A modem transmits a +2 voltage signal into a channel. The channel adds to this signal a noise
term that is drawn from the set
{0, −1, −2, −3}
with respective probabilities
{
ସ
ଵ
,
ଷ
ଵ
,
ଶ
ଵ
,
ଵ
ଵ
}
.
a)
Find the pmf of the output
ܻ
of the channel.
b)
What is the probability that the output of the channel is equal to the input of the
channel?
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 Spring '11
 Prof.ShenghuiSong
 Probability theory, cherry bits, red cherry bits, green cherry bits

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