Random Variable Problems? Can someone show me how to work this out? I can't get the answers in the boxes. 

Let's $Y$ be the number of spots on the dice.
Then:
$$Y = 1 \Rightarrow X = (1 - 4)^2 = 9$$
$$Y = 2 \Rightarrow X = (2 - 4)^2 = 4$$
$$Y = 3 \Rightarrow X = (3 - 4)^2 = 1$$
$$Y = 4 \Rightarrow X = (4 - 4)^2 = 0$$
$$Y = 5 \Rightarrow X = (5 - 4)^2 = 1$$
$$Y = 6 \Rightarrow X = (6 - 4)^2 = 4$$
You can write that:
$$P(X = 0) = \frac{1}{6}$$
$$P(X=1) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6}$$
$$P(X=4) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6}$$
$$P(X=9) = \frac{1}{6}$$
Also, $P(X = k) = 0$ for all $k \not \in \{0, 1, 4, 9\}$.
Now you have all the ingredients you need to finish the exercise yourself.
