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Massachusetts
Institute
of
Technology
Department
of
Electrical
Engineering
&
Computer
Science
6.041/6.431:
Probabilistic
Systems
Analysis
(Spring
2010)
Problem
Set
1
Due:
September
15,
2010
1.
Express
each
of
the
following
events
in
terms
of
the
events
A
,
B
and
C
as
well
as
the
operations
of
complementation,
union
and
intersection:
(a)
at
least
one
of
the
events
A
,
B
,
C
occurs;
(b)
at
most
one
of
the
events
A
,
B
,
C
occurs;
(c)
none
of
the
events
A
,
B
,
C
occurs;
(d)
all
three
events
A
,
B
,
C
occur;
(e)
exactly
one
of
the
events
A
,
B
,
C
occurs;
(f)
events
A
and
B
occur,
but
not
C
;
(g)
either
event
A
occurs
or,
if
not,
then
B
also
does
not
occur.
In
each
case
draw
the
corresponding
Venn
diagrams.
2.
You
ﬂip
a
fair
coin
3
times,
determine
the
probability
of
the
below
events.
Assume
all
sequences
are
equally
likely.
(a)
Three
heads:
HHH
(b)
The
sequence
head,
tail,
head:
HTH
(c)
Any
sequence
with
2
heads
and
1
tail
(d)
Any
sequence
where
the
number
of
heads
is
greater
than
or
equal
to
the
number
of
tails
3.
Bob
has
a
peculiar
pair
of
foursided
dice.
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 Fall '10
 Prof.DimitriBertsekas
 Electrical Engineering, Probability, Probability theory, Probabilistic Systems Analysis, Department of Electrical Engineering & Computer Science

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