Adding R File, Day 4

MonteCarlo.R

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+out<- rnorm(1000, mean = 0, sd = 5)
+
+means<- cumsum(out)/(1:len(out))
+
+plot(means, pch ='', xlab='Number of Draws', ylab='Estimate', ylim=c(-10, 10))
+abline(h =0 , col=gray(0.5), lwd = 4)
+points(means, type='l', lwd = 1.5)
+
+dev.copy(device=pdf,file='~/dropbox/teaching/pol350a/mclass5/MonteCarloExample.pdf', height=6, width = 6)
+dev.off()
+
+##showing how this can vary over many trials
+
+
+
+plot(means, pch ='', xlab='Number of Draws', ylab='Estimate', ylim=c(-10, 10))
+abline(h =0 , col=gray(0.5), lwd = 4)
+
+
+
+for(z in 1){
+	start<- rnorm(1000, mean = 0, sd = 5)
+	means<- cumsum(start)/(1:len(start))
+	points(means, type='l', lwd = 1.5, col='black')
+}
+
+
+dev.copy(device=pdf,file='~/dropbox/teaching/pol350a/mclass5/MonteCarloExample1.pdf', height=6, width = 6)
+dev.off()
+
+
+plot(means, pch ='', xlab='Number of Draws', ylab='Estimate', ylim=c(-10, 10))
+abline(h =0 , col=gray(0.5), lwd = 4)
+
+
+
+for(z in 1){
+	start<- rnorm(1000, mean = 0, sd = 5)
+	means<- cumsum(start)/(1:len(start))
+	points(means, type='l', lwd = 1.5, col='black')
+}
+
+
+dev.copy(device=pdf,file='~/dropbox/teaching/pol350a/mclass5/MonteCarloExample2.pdf', height=6, width = 6)
+dev.off()
+
+
+
+##working with the uniform random variable
+
+##what is prob(x \in [0.2, 0.6])?
+
+##analytically,  prob(x \in [0.2, 0.6]) = \int_{0.2}^{0.6} 1 dx = 0.4
+
+##via monte carlo simulation we can count the proportion of draws that fall between 0.2 and 0.6
+
+
+draws<- runif(10000, 0, 1)
+estimate<- cumsum(ifelse(draws < 0.6 & draws>0.2, 1, 0))/(1:len(draws))
+
+plot(estimate,pch ='', xlab = 'Number of Draws', ylab='Estimate')
+abline(h = 0.4, lwd = 3, col=gray(0.5))
+points(estimate, type='l', lwd = 1.5)
+
+
+
+
+
+