EL6303
HW 4.1
1. X is uniform in (-2,1) and Y X . Find and draw
fY ( y) and FY ( y) .
2
Solution:
y x2
4
1/ 3
f X ( x)
1
2 1
1
x
x
2
1
fY ( y ) 0, for y 0 and for y 4.
For 0 y 1, there are two roots :
y g ( x) x 2 x y
f ( x ) f ( x ) (1/ 3) (1/ 3)
1
fY (

HW 4.2 Part 2
1. rv mapping
Let y be a random variable with probability density function
f(y)=0.5*sin(y) wherey0. Let x be a random variable uniformly
distributed in the interval: [0 1].
Find a mapping function from x to y.
(hint: Express y in terms of x