(a) For each value of X we have:
[tex]X=0\quad\Rightarrow\quad Y=4\\\\X=1\quad\Rightarrow\quad Y=-23\\\\X=2\quad\Rightarrow\quad Y=-32\\\\X=3\quad\Rightarrow\quad Y=-23\\\\X=4\quad\Rightarrow\quad Y=4\\\\X=5\quad\Rightarrow\quad Y=49[/tex]
so the range of Y = {-32, -23, 4, 49}
(b)
[tex]P\{Y=4\}=P\{X=0\}+P\{X=4\}=0.00032+0.4096=\boxed{0.40992}[/tex]
(c)
Y cannot equal 0, so
[tex]P\{Y=0\}=0[/tex]
