Please answer all parts to the question below, I will upvote!

(#4) Suppose that a random variable X has a Poisson distribution with unknown mean 0-. (7 POINTS) (I) Write the pmf / pdf of X. (II) Write out the following function in simplified form. A (X10) = In [f (X10 )] = (III) Write out the following function in simplified form. (IV) Write out the following function in simplified form. A" (Xle) _ -a(xle) (V) Write out the Fisher Information for e in X in simplified form. I (0) =- ED" (X10)] =