problem 1: Suppose you flip 6 coins, what is the probability 2 of them are heads? Simulate 10000 batches and refresh several times to get an eyeball average.
problem 2: Suppose you flip 8 coins, what is the probability 4 of them are heads? Simulate 10000 batches and refresh several times to get an eyeball average.
problem 3: A particular share has a distribution with an average return of 0.007 per month, with standard deviation of 0.08 per month. What percentage of the time will this portfolio at least break even? For simplicity add the 12 monthly returns to each other to get the annual return." Use 1000 different years for your simulation and take an eyeball average of the number greater than zero.
problem 4: You are the manager of an amusement park with a popular roller coaster. Guests arrive randomly to the ride and an average rate of 2300 people per hour with a standard deviation of 400 people per hour. The ride has a constant throughput of 2300 people per hour. The park is open from 10 a.m. to 10 p.m. If you were to check how many people were in line at the end of every hour, what would the average number of people be? Use 100,000 rows for your simulation.
problem 5: You are the owner/operator of a newspaper stand. The papers cost $0.10 to print and sell for $0.55. Typical demand averages 210 papers with a standard deviation of 20. If you order 230 papers, how much profit can you expect per day, on average? Use 100,000 rows for your simulation.
problem 6: Consider an investor who plans on putting $1000 in a Dow Jones industrial average index fund. The Dow Jones has historically returned 0.005265074 per month with a standard deviation of 0.053730335 per month. What is the probability the balance at withdrawal 12 months later is less that $1050? To find out this, use the following formula: New Value = Old Value * (1 + return) Simulate 1000 different years of Dow Jones data and then check each individual year to see whether the investor has more than that amount at the end using an = if() statement.