sm8_7

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Problem 8.7 What is the probability density function of the random variable Y of Example 8.8? Sketch 
this density function. 
 
Solution 
From Example 8.8, the distribution of Y is 
( ) ( )
⎪⎪⎩
⎪⎪⎨
⎧
>
<−
−<
=
−
11
1||
2
cos22
10
1
y
yy
y
yFY π
π 
 
Thus, the density of Y is given by 
 
( )
⎪⎪⎩
⎪⎪⎨
⎧
>
<−
−<
=
10
1||
1
1
10
2
y
y
y
y
dy
ydFY
π 
 
This density is sketched in the following figure. 
1-1
y
fY(y)
π
1
 
 
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