### Filename: Normal1_2008.R ### Paul Johnson March 31, 2008 ### This code should be available somewhere in http://pj.freefaculty.org. If it is not ### email me mymean <- 0 mystd <- 1.5 myx <- seq( mymean - 3*mystd, mymean+ 3*mystd, length.out=500) myDensity <- dnorm(myx,mean=mymean,sd=mystd) plot(myx, myDensity, type="n", xlab="X", ylab="Probability Density ") lines(myx,myDensity,lty=4, col=4) ### change line type & color if you want #maybe broaden out x myx <- seq( mymean - 6*mystd, mymean+ 6*mystd, length.out=500) myDensity <- dnorm(myx,mean=mymean,sd=mystd) plot(myx, myDensity, type="n", xlab="X", ylab="Probability Density ") lines(myx,myDensity,lty=4, col=4) ### change line type & color if you want par(mfcol=c(2,1)) plot(myx, myDensity, type="n", xlab="X",ylab="Probability Density Function") lines(myx, myDensity ) myCumulProb <- pnorm(myx, mean=mymean, sd=mystd) plot(myx, myCumulProb, type="n", xlab="X", ylab="Cumulative Distribution Function") lines(myx,myCumulProb,lty=4, col=4) ### change line type & color if you want par(mfcol=c(1,1)) # What does one random sample from this distribution look like? mySample <- rnorm(50, mean = mymean, sd = mystd) hist(mySample, freq=FALSE, xlab="x", main="Histogram and Density of one Sample") hist(mySample, freq=FALSE, xlab="x", main="Histogram and Density of one Sample", breaks=20) lines(density(mySample)) # Compare against true probabilities ## 4 lines simply re-do previous 4, in case you closed the graph already. mySample <- rnorm(50, mean = mymean, sd = mystd) hist(mySample, freq=FALSE, xlab="x", main="Histogram and Density of one Sample", breaks=20) lines(density(mySample)) xrange <- seq(min(mySample), max(mySample), by=0.1) trueProbs <- dnorm(xrange,mean=mymean,sd=mystd) lines( xrange, trueProbs, lty=6, col=4, lwd=2) hist (mySample, freq=F, xlab="X", main= paste("Normal Sample (50 Observations)\n Mean=", mymean, "Std.Dev=", mystd)) t1 <- bquote( mu== .(mymean)) t2 <- bquote( sigma== .(mystd)) hist (mySample, freq=F, xlab="X", main= t1 ) mtext(t2, 3)