romputer compute iu.,tead
E
lO
(n

1Jx)px(n).
last
tWD
fiips
of the coin. (For in8tanre,
for
the outcome
hht.
~
have
X
=
2.
What nwnerical
ans~r
did the comput.er give
her"
(Explain your
an~~r
Y
=
I,
and (or
the
outcome
tth
we
have
X
=
0,
Y
=
1.)
Provide
a
table
that
carefully.)
gi~
the
joint distribution o(
X
and
Y,
i.e.,
a
tfLble
that
gives
the nwnbers
P(X
=
k, Y
=
I),
k
=
D,
1,2,
t
=
0,1,2.
(The numbers
in
the
tfLble
should
be given
8B
(rsction~,
or
in
decimal (onn.) (Show and explain
yoUr
work.)
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points) A continuous random variable
X
has probability density
12) (10
points)
A
continuous random variable
Y
has probabiJity deIl8ity
(unc
function given below, where
C
is
an appropriate number.
tion given below.
Olf'<O'
0
if
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or
s>l,
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Cs
if
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1
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.,
<
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{
{
Cs
3
1f
lJ
~
1.
1 
s
if
0
s:
H
s:
1.
Find
the
value of
C
Md
compute the
mean
1lX
of
X.
(Provide llwnerical
Clmpute
Va.r(Y).
(Provide a numerical answer in decimal (orm.) (Show
snd
answers
in
decima.l
fOffi'l.)
(Shvw and
p,Xplain
your
'\\'Ork.)
e>..plsin
your work.)
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