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Monte Carlo Integration
set.seed(100) ####################################### ## Monte Carlo simulation for estimating ## integral (3x^2 + 5x)_0^1 ####################################### # True value is 3.5 true <- 3.5 # 1. Set n # 2. Generate n Uniform[0,1] # 3. Find mean of g(x) = 3x^2 + 5x n <- 10 samp <- runif(n = n, min = 0, max = 1) gx <- 3*samp^2 + 5*samp mean(gx) # Repeating for larger n n <- 100 samp <- runif(n = n, min = 0, max = 1) gx <- 3*samp^2 + 5*samp mean(gx) n <- 1000 samp <- runif(n = n, min = 0, max = 1) gx <- 3*samp^2 + 5*samp mean(gx) # Make a running plot of the estimate n <- 5e3 samp <- runif(n = n, min = 0, max = 1) gx <- 3*samp^2 + 5*samp plot.ts(cumsum(gx)/(1:n), ylab = "Running Average", xlab = "n") abline(h = true, col = "red")
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