To calculate E[Y+4] and Var[3Y] for the given probability distribution.

The problem asks to calculate $E[Y+4]$ and $Var[3Y]$ for the given probability distribution.

First, let's verify the sum of probabilities:

$$P(Y=0) + P(Y=1) + P(Y=2) + P(Y=3) + P(Y=4)$$ $$= \frac{1}{8} + \frac{19}{84} + \frac{1}{6} + \frac{5}{168} + \frac{7}{24}$$

To sum these, we find the least common multiple (LCM) of the denominators (8, 84, 6, 168, 2