par(mar = c(3.5, 3.5, 1.5, 0.5)) x <- c(168,161,167,179,184,166,198,187,191,179) plot(ecdf(x), verticals = TRUE) xp <- seq(0.9*min(x), 1.1*max(x), length.out = 100) lines(xp, pnorm(xp, mean(x), sd(x))) punif(30,0,30)-punif(20,0,30) 1-punif(30,0,30) pnorm(-2) pnorm(-2) z=seq(-4,4,by=0.01) plot(z,dnorm(z),type="l",xaxt="n",yaxt="n") polygon(c(-2,seq(-2,-4.3, by=-0.01),-4.4,-2),c(0,dnorm(seq(-2,-4.3, by=-0.01)),0,0),col="pink") axis(1, at=-3:3, labels=-3:3) 1-pnorm(2) z=seq(-4,4,by=0.01) plot(z,dnorm(z),type="l",xaxt="n",yaxt="n") polygon(c(2,seq(2,4.3, by=0.01),4.4,2),c(0,dnorm(seq(2,4.3, by=0.01)),0,0),col="pink") axis(1, at=-3:3, labels=-3:3) pnorm(1)-pnorm(-1) z=seq(-4,4,by=0.01) plot(z,dnorm(z),type="l",xaxt="n",yaxt="n") polygon(c(1,seq(1,-4.3, by=-0.01),-4.4,1),c(0,dnorm(seq(1,-4.3, by=-0.01)),0,0),col="red") axis(1, at=-3:3, labels=-3:3) pnorm(1)-pnorm(-1) z=seq(-4,4,by=0.01) plot(z,dnorm(z),type="l",xaxt="n",yaxt="n") polygon(c(1,seq(1,-4.3, by=-0.01),-4.4,1),c(0,dnorm(seq(1,-4.3, by=-0.01)),0,0),col="red") polygon(c(-1,seq(-1,-4.3, by=-0.01),-4.4,-1),c(0,dnorm(seq(-1,-4.3, by=-0.01)),0,0),col="grey") axis(1, at=-3:3, labels=-3:3) 1-pnorm(300, m = 280, s = 10) 1-pnorm((300-280)/10) z=seq(-4,4,by=0.01) plot(z,dnorm(z),type="l",xaxt="n",yaxt="n") polygon(c(2,seq(2,4.3, by=0.01),4.4,2),c(0,dnorm(seq(2,4.3, by=0.01)),0,0),col="pink") axis(1, at=-3:3, labels=seq(250,310, by=10)) 1-pnorm(300, m = 290, s = 4) z=seq(-4,4,by=0.01) plot(z,dnorm(z),type="l",xaxt="n",yaxt="n") polygon(c(2.5,seq(2.5,4.3, by=0.01),4.4,2.5),c(0,dnorm(seq(2.5,4.3, by=0.01)),0,0),col="pink") axis(1, at=-3:3, labels=seq(278,302, by=4)) qnorm(c(0.025, 0.975), m = 290, s = 4) 1-pexp(2, rate = 1/2) z=seq(0,8,by=0.01) plot(z,dexp(z, 1/2),type="l", main="Exp(2) - distribution") polygon(c(2,seq(2,8, by=0.01),8,2),c(0,dexp(seq(2,8, by=0.01),1/2),0,0),col="pink") text(3,0.07,"P(X>2)") text(3,0.03,"=0.37") polygon(c(2,seq(2,0, by=-0.01),0,2),c(0,dexp(seq(2,0, by=-0.01),1/2),0,0),col="grey") text(1,0.1,"P(X<2)") text(1,0.05,"=0.63") ## z=seq(0,8,by=0.01) ## ## ## plot(z,dexp(z, 1/2),type = "l", main = "Exp(2) - distribution") ## ## ## polygon(c(2, seq(2, 8, by = 0.01), 8, 2), ## ## c(0, dexp(seq(2, 8, by = 0.01), 1/2), 0, 0), ## ## col = "pink") ## ## ## text(3,0.07,"P(X>2)") ## ## text(3,0.03,"=0.37") ## ## ## polygon(c(2, seq(2, 0, by = -0.01), 0, 2), ## ## c(0, dexp(seq(2, 0, by =- 0.01), 1/2), 0, 0), ## ## col = "grey") ## ## ## text(1,0.1,"P(X<2)") ## ## text(1,0.05,"=0.63") dpois(0,1) exp(-1) dpois(0,5) 1-pnorm(4000, m = 3850, s = sqrt(5500)) 1-pnorm(4000, m = 3850, s = 550)