(3) Let $Y_1, Y_2, ..., Y_n$ denote a random sample from a pdf given by (for 0 < y)
$$f(y; \theta) = 3\theta e^{(-3\theta)y}$$
i. Find $E[Y + 5]$. {Hint: This is a Gamma dist.}
ii. What is the method of moment estimator of $\theta$.
iii. Suppose that $y_1 = 0.30, y_2 = 0.36, y_3 = 0.20, and y_4 = 0.25$ are realizations from this pdf. What is the method of moments estimate of $\theta$.
