Exercise 2. American Roulette Monte Carlo simulation

Create a Monte Carlo simulation that generates 10,000 outcomes of \(S\), the sum of 100 bets.

Compute the average and standard deviation of the resulting list and compare them to the expected value (-5.263158) and standard error (40.19344) for \(S\) that you calculated previously.

This exercise is part of the course

HarvardX Data Science - Probability (PH125.3x)

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Exercise instructions

Use the replicate function to replicate the sample code for B <- 10000 simulations.
Within replicate, use the sample function to simulate n <- 100 outcomes of either a win (17) or a loss (-1) for the bet. Use the order c(17, -1) and corresponding probabilities. Then, use the sum function to add up the winnings over all iterations of the model. Make sure to include sum or DataCamp may crash with a "Session Expired" error.
Use the mean function to compute the average winnings.
Use the sd function to compute the standard deviation of the winnings.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Assign a variable `p_green` as the probability of the ball landing in a green pocket
p_green <- 2 / 38

# Assign a variable `p_not_green` as the probability of the ball not landing in a green pocket
p_not_green <- 1-p_green

# Define the number of bets using the variable 'n'
n <- 100

# The variable `B` specifies the number of times we want the simulation to run. Let's run the Monte Carlo simulation 10,000 times.
B <- 10000

# Use the `set.seed` function to make sure your answer matches the expected result after random sampling.
set.seed(1)

# Create an object called `S` that replicates the sample code for `B` iterations and sums the outcomes.




# Compute the average value for 'S'


# Calculate the standard deviation of 'S'

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