week 7
1
Functions of Random variables
•
In some case we would like to find the distribution of
Y
=
h
(
X
) when the
distribution of
X
is known.
•
Discrete case
•
Examples
1. Let
Y
=
aX
+
b
,
a
≠
0
2. Let
( )
(
)
(
)
(
)
( )
(
)
(
)
(
)
∑
−
∈
−
=
=
∈
=
=
=
=
=
y
h
x
Y
x
X
P
y
h
X
P
y
X
h
P
y
Y
P
y
p
1
1
(
)
(
)
(
)
⎟
⎠
⎞
⎜
⎝
⎛
−
=
=
=
+
=
=
b
y
a
X
P
y
b
aX
P
y
Y
P
1
2
X
Y
=
(
)
(
)
(
)
(
)
(
)
⎪
⎩
⎪
⎨
⎧
<
=
=
>
−
=
+
=
=
=
=
=
0
0
0
0
0
2
y
if
y
if
X
P
y
if
y
X
P
y
X
P
y
X
P
y
Y
P

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*