Please answer question 3 and 4 in the first picture and the question for extra credit in the next picture

Extra Credit. The PDF of the Gannna distribution with parameters or :3- D and ,3 3* is given by 1 maIEsf rs) = MW , {You can think of Ho) as the constant such that at) integrates to 1. The denition [To] = If ra'le'mdzs is not needed for this problem.) Suppose X is a Gamma random variable with parameters or and ,6, where e: is a positive integer and ,8 = 1. Suppose that Y is a Poisson random variable with parameter A. Prove that PD: 13 A] = P[Y i: or 1]. $310. 3. Which of the following are probability density functions? Find c and the corresponding cumulative distribution function F(x) for those that are. (a) f (x ) = 0 , ex, if x > 1, otherwise. (Hint: the answer depends on different values of the given constant d.) (b) f(x) = ce"(1 + ex)-2, for -00