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Let's build a simulation to understand the difference between the number of steps in a simulation versus the number of runs in a Monte Carlo experiment.
Q: Build a model to determine the average move in Monopoly (two dice).
Q: Build a model to determine the average move in a two-dice game where you get to roll one more time if you get doubles.
Q: Build a model to determine the average move in a two-dice game where you get to keep rolling if you get doubles. (This is tricky! First think about it mathematically.)
Q: Build a model to determine the average bank balance over 10 years at 5 percent compounded yearly and annual deposits that are random between 50 and 100 dollars.
Q: Use a Monte Carlo experiment with 100 trials to determine the mean and variance.
Q: A survey of households asked how many telephones are in the house, and found the following data. What is the mean, median and mode of the following:
value prob 1 0.1 2 0.30 3 0.35 4 0.10 5 0.10 6 0.05
What if we switched the 0.35 and the 0.30?
Q: What is the variance? The standard deviation?
Q: Can you think of any flaws in this survey?
Q: Create a stem-and-leaf diagram of the following data.
48, 33, 43, 42, 51, 20, 58, 19, 33, 31, 70, 52, 56, 45, 74, 25, 49, 64, 55, 30, 40, 49, 24, 49, 41, 62, 52, 57, 60, 53,
Q: How would you make a histogram (bar chart) of this data in Excel?
Q: Make a box-and-whisker plot of the data above.
Q: What is an ogive? How would you make one?
Q: A student has gotten the following grades:
homework 1: 92
homework 2: 96
homework 3: 84
midterm: 88
What is her average? What is her average if homeworks are worth 40 percent and exams worth 60 percent?
Q: In a restaurant, you can order your burrito:
Q: If four people line up to get a burrito, how many different sequences of people are there? Sequences of orders? What if they arrange not to have any repeated orders (it's so embarrassing to say "I'll have the same.").
Q: If there are 15 questions on the exam, in how many different orders can you finish them? Suppose I say "do any 10 of the questions." How many different ways are there to take the exam?
Q: If the probability of heads is 60 percent, and the probability of black is 45 percent, what is:
Q: If the probability of Peter Jackson winning best director was 40 percent, and the probability that Lord of the Rings: The Return of the King winning best picture was 30 percent, what was the probability that either event would occur.
Q: If the probability that he would win best director given that LotR:RotK wins best picture is 80 percent, what is the probability that he will win both awards?
Q: If the probability of each academy award is independent of the others, and we assume that each movie has the same probability of winning, what is the probability that LotR will sweep all 11 awards? Note that LotR had 4 competitors in each category except Makeup (2 competitors), Visual Effects (2).
Q: What's the probability of a bridge hand with no aces?
Q: What's the probability of hitting safely in a baseball game, if your probability of hitting safely at each of your 4 at-bats is 1/3?
Q: If a hotline call center gets 0.3 calls per hour, what's the probability that there will be no calls in a 4-hour shift?
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