Problem 8 [Bonus]: (6 Points} Let Z be the standard normal random variable1 and dene the function a} {2 Points} Evaluate the following two limits: um L{z) zioo and lil L{z} zIoo b) (4 Points) Suppose you are rlmning a business, and you estimate your prot to be normally distributed with mean a = 1000 and standard deviation 0* = 400. But1 if your prots are negative then you will declare bankruptcy and your prot will instead be zero. What will your expected prot be? Give your answer in terms of the L{z) function and the cdf of the standard normal Ma], and do not try to evaluate these functions. {For example1 your nal answer could be that the expected prot is 2L(4] + gb[1))