1. mean(pe$age) 2. dbeta(0.75,0.2,0.2) / (1 - pbeta(0.75,0.2,0.2)) # 0.970 3. 1 - 2 * pnorm(-1.80,0,1) # 0.928 4. Cov(X1,X2) = E(X1 X2) - EX1 EX2 EX1 = EX2 = (69+72+70) / 3 = 70.333 E(X1 X2) = (69*72 + 69*70 + 72*70) / 3 = 4946 4946 - 70.333^2 -0.778 5. simCI <- function(nreps) { tmp <- replicate(nreps,findCI()) trueConfLevel <- mean(tmp) return(trueConfLevel) } # form CI and see if it contains 1.0, the pop. mean findCI <- function() { x <- rexp(10,rate=1.0) # our sample center <- mean(x) # X-bar s <- sd(x) * sqrt(9/10) radius <- 1.96 * s / sqrt(10) abs(center - 1.0) < radius } # 0.854