Problem
Set
1
MAS
622J/1.126J:
Pattern
Recognition
and
Analysis
Due
Monday,
18
September
2006
[Note:
All
instructions
to
plot
data
or
write
a
program
should
be
carried
out
us
ing
either
Python
accompanied
by
the
matplotlib
package
or
Matlab.
Feel
free
to
use
either
or
both,
but
in
order
to
maintain
a
reasonable
level
of
consistency
and
simplicity
we
ask
that
you
do
not
use
other
software
tools.]
Problem
1:
Why?
a.
Describe
an
application
of
pattern
recognition
related
to
your
research.
What
are
the
features?
What
is
the
decision
to
be
made?
Speculate
on
how
one
might
solve
the
problem.
Limit
your
answer
to
a
page.
b.
In
the
same
way,
describe
an
application
of
pattern
recognition
you
would
be
interested
in
pursuing
for
fun
in
your
life
outside
of
work.
X
Problem
2:
Probability
WarmUp
Let
X
and
Y
be
random
variables.
Let
µ
X
≡
E[
X
]
denote
the
expected
value
of
X
and
σ
2
≡
E[(
X
−
µ
X
)
2
]
denote
the
variance
of
X
.
Use
excruciating
detail
to
answer
the
following:
a.
Show
E[
X
+
Y
]
=
E[
X
]
+
E[
Y
].
X
b.
Show
σ
2
=
E[
X
2
]
−
µ
2
.
X
2
are uncorrelated, then
σ
Z
c.
Show
that
independent
implies
uncorrelated.
d.
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 Fall '00
 KevinAmaratunga
 Variance, Probability theory, probability density function, Monty Hall

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