Shawn Bishop, a neuroscience PhD student at Clarksville University, has been having problems balancing his checkbook. His monthly income is derived from a graduate research assistant ship; however, he also makes extra money in most months by tutoring undergraduates in their introductory neurobiology course. His chances of various income levels are shown here (assume that this income is received at the beginning of each month):

Bishop has expenditures that vary from month to month, and he estimates that they will follow this distribution:

Bishop begins his final year with $1,500 in his checking account. Simulate the cash flow for 12 months and replicate your model N times to identify Bishop€™s (a) ending balance at the end of the year and (b) probability that he will have a negative balance in any month.

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PROBABILITY 0.35 0.25 0.25 0.15 MONTILY INCOME 850 900 950 $1,000 MONTHLY EXPENSES $ 800 $ 900 $1,000 $1,100 PROBABILITY 0.05 0.20 0.40 0.35