create a function for central theroem limit in r

The central limit theorem states that, under certain conditions, the distribution of the sample means approximates a normal distribution as the sample size gets larger. In R, we can create a function that simulates this process by generating random samples and calculating their means.

Here's an example function that implements the central limit theorem in R:


main.r
central_limit <- function(n, m, s, r) {
  # n: sample size
  # m: population mean
  # s: population standard deviation
  # r: number of samples to generate
  
  # Generate r random samples, each of size n
  samples <- replicate(r, rnorm(n, m, s))
  
  # Calculate the means of each sample
  sample_means <- apply(samples, 2, mean)
  
  # Plot the distribution of sample means
  hist(sample_means, main = "Distribution of Sample Means",
       xlab = paste0("Sample Size: ", n, ", Number of Samples: ", r),
       breaks = 30, probability = TRUE)
  
  # Add a normal curve to the plot
  x <- seq(min(sample_means), max(sample_means), length = 100)
  y <- dnorm(x, m, s/sqrt(n))
  lines(x, y, col = "red", lwd = 2)
}
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You can use this function to simulate the central limit theorem for different combinations of sample size, population mean, and standard deviation. For example, to generate 100 samples of size 30 from a population with mean 50 and standard deviation 10, you can call:


main.r
central_limit(n = 30, m = 50, s = 10, r = 100)
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This will generate a histogram of the sample means with a red line representing the normal distribution approximation.

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central limit theorem