# Run commands by highlighting a section and clicking

# "Run" in the top right corner of the "script" window. Run commands in ORDER.

# Create a vector of wheel outcomes and their frequency on the wheel.

# The command c() combines values into a vector. Each value must be separated by a comma.

# The rep(x,times) repeats whatever x is however many times you want it to.

Wheel.Outcomes = c(rep(0,2), rep(300,5),

rep(350,1),rep(400,2),

rep(450,1),rep(500,3),

rep(550,1),rep(600,3),

rep(700,1),rep(800,2),

rep(900,2),rep(5000,1))

barplot(table(Wheel.Outcomes)/24, main = "PMF for Spin Outcome", col = rainbow(12))

# Start simulation.

# Part 3a. ########################################################

# Spin the wheel 1 time. Samples the vector 1 time.

sample(Wheel.Outcomes, 1, replace = TRUE)

# This code "Spins the wheel" 1000 times.

# Actually, samples the Wheel.Outcomes vector 1000 times with replacement.

# Makes a new vector of 1000 spin outcomes.

spins.thousand = sample(Wheel.Outcomes, 1000, replace = TRUE)

# Part 3b. ########################################################

# Expected Dollar Amount. How does this compares to part 2d?

mean(spins.thousand)

# The table command counts the number of spins from each amount.

table(as.factor(spins.thousand))

# Part 3c. #######################################################

# Divide the counts by 1000.

# This is the Simulated Probability Mass Function.

# How does it compare to the one you created in part 2a?

table(as.factor(spins.thousand))/1000

# Check out the probability mass function in a plot. Copy and paste this plot to DA.

# Do the simulated values see to match the theoretical ones?

barplot(table(as.factor(spins.thousand))/1000, col = rainbow(12), main = "Simulated PMF of Wheel Spin Outcomes")

# Optional: You can run the simulation as many times as you want. # You can also increase or decrease the number of spins.

The PMF in Part 2 is based on probability theory. Do these probabilities stand up when a contestant actually spins the wheel? Go back to the Data Analysis #1 instructions page on Canvas, download the R script titled: Wheel_of_Fortune_Spin_Script.R , open the file it will automatically open in R. You need R software on the computer to open the script window. Follow the instructions in the code then answer the following: a. (1 point) What value did you spin?

b. (1 point) What is the average of the 1000 simulated spins? How does this value compare to your answer in part 2c? c. (1 point) Include the simulated probability mass function AND the plot of the probability mass function from R. For the probability mass function, you should include a table with the all possible outcomes and the proportion of times each outcome was spun (output from line 43 of the code). d. (1 point) How different are the simulated probabilities to the theoretical probabilities in part 2? e. (1 point) Based on the plot are the least likely outcomes the same as it is in part 2a? f. (1 point) In general, what action will make the simulated values more like the theoretical ones?