The probability mass function of a random variable $Y$ is given by
$$f(y) = \frac{a^{(y-3)}}{(e^a)(y-3)!} \quad \text{for } y = 3,4,\dots\text{ and } a > 0$$
Derive the cumulant generating function of $Y$ and use it to obtain the kurtosis of $Y$
I think you need to use some sort of substitution to transform this into a pmf (eg $x = y - 3$) but I'm just not sure how exactly to account for the substitution.