monterey carlo model coin flips in r

To simulate coin flips and run a Monte Carlo simulation in R using the binomial distribution, follow these steps:

1. Set the number of flips per trial and the number of trials:

num_flips <- 10
num_trials <- 1000
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2. Use the rbinom function to simulate coin flips. This function generates random numbers from the binomial distribution with a given number of trials and probability of success. In this case, we'll set the probability to 0.5 (since the coin is fair).

coin_flips <- rbinom(num_trials, num_flips, 0.5)
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3. Calculate the mean and standard deviation of the number of heads per trial:

mean_heads <- mean(coin_flips)
sd_heads <- sd(coin_flips)
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4. Plot a histogram of the number of heads per trial:

hist(coin_flips, breaks = seq(0, num_flips + 1), 
     col = "lightblue", xlab = "Number of Heads", 
     main = "Histogram of Coin Flips")
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5. Calculate the probability of getting a certain number of heads or fewer:

prob_5_or_fewer <- sum(coin_flips <= 5) / num_trials
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This is just a basic example of how to simulate coin flips and run a Monte Carlo simulation in R. You can adjust the number of flips per trial and the number of trials to get different results. You can also experiment with different probabilities of success.