#-----------------------------------------------------# #--- Classical and Bayesian inference (AMS132) ---# #--- Class 14 ---# #-----------------------------------------------------# # P(hat(sigma^2) < sigma^2 ): n <- 10 pchisq(n, df=n-1) # joint probability of sample meana and sample standars deviation: probs <- c() for(n in 2:50){ p1 <- pnorm(sqrt(n)/5, 0, 1)-pnorm(-sqrt(n)/5, 0, 1) p2 <- pchisq(36*n/25, df=n-1)-pchisq(16*n/25, df=n-1) probs[n] <- p1*p2 } plot(2:50, probs[2:50]) abline(h=0.5, col="red", lwd=3) abline(v=021, col="blue", lwd=3)