The AMS is running a fundraiser by selling lottery tickets for $2 each. Each ticket indepen- dently has a 1/50 chance of winning $95. A student with just $10 decides that they will purchase one ticket each day. They decide that they will stop if they either win once (i.e., they will not purchase more tickets), or until they run out of money. a) Provide the probability distribution of the student's final net gain (give a table of possible values and their associated probabilities). Keep probabilities to 4 siginficant figures. (2.5 marks) b) What is the expected value of the student's strategy? The standard deviation? (2 marks) c) Suppose the student has $ 200 instead, and spends this all on lottery tickets, regardless of the outcome. What is the expected value and standard deviation of the net gain of this new strategy? (2.5 marks) d) Approximately compute the probability that the student makes a profit from this new strategy. (hint: use Poisson approximation to Binomial rv) (3 marks