Question

Suppose that X is a random variable with probability function x 0 1 2 3 4 5 P(x) 0.00032 0.0064 0.0512 0.2048 0.4096 0.32768 and that the random variable Y = 9X2 − 36X + 4. (a) What is the range of Y ? (b) Calculate P{Y = 4}. (c) Calculate P{Y = 0}.

Answer 1

(a) For each value of X we have:

$X=0\quad\Rightarrow\quad Y=4\\\\X=1\quad\Rightarrow\quad Y=-23\\\\X=2\quad\Rightarrow\quad Y=-32\\\\X=3\quad\Rightarrow\quad Y=-23\\\\X=4\quad\Rightarrow\quad Y=4\\\\X=5\quad\Rightarrow\quad Y=49$

so the range of Y = {-32, -23, 4, 49}

(b)

$P\{Y=4\}=P\{X=0\}+P\{X=4\}=0.00032+0.4096=\boxed{0.40992}$

(c)

Y cannot equal 0, so

$P\{Y=0\}=0$