Suppose that you have $200,000 to invest in stocks. If you invest $1000 in any particular stock, your prot will be equal in distribution to X where is uniform on [$100; $0; $100; $200]. Suppose that there are 200 distinct stock that behave independently.
(a) Suppose that you invest the entire $200,000 in one stock. Find the probability that the prot will be more than $16,000.
(b) Suppose that you invest the $1,000 each in 200 distinct stocks. Estimate the probability that the prot will be more than $16,000.