#prior first scientist#
sd0 <- 20
phi0 <- sd0^2
theta0 <- 370
z=seq(200,600,by=1)
y0=dnorm(z,theta0,sd0)
plot(z,y0,type="l",ylim=c(0,0.054))

#likelihood#
sdobs <- 8
phi <- sdobs^2
x <- 421

#posterior first scientist#
phi1 <- (phi0^(-1) + phi^(-1))^(-1)
sd1 <- sqrt(phi1)
theta1 <- phi1*(theta0/phi0 + x/phi)
cat("First scientist has posterior mean",theta1,"and s.d.",sd1,".\n")
y1=dnorm(z,theta1,sd1)
lines(z,y1)

#prior second scientist# 
sd0hat <- 50
phi0hat <- sd0hat^2
theta0hat <- 400
y0hat=dnorm(z,theta0hat,sd0hat)
lines(z,y0hat,lty=4)

#posterior second scientist#
phi1hat <- (phi0hat^(-1) + phi^(-1))^(-1)
sd1hat <- sqrt(phi1hat)
theta1hat <- phi1*(theta0hat/phi0 + x/phi)
cat("Second scientist has posterior mean",theta1hat,"and s.d.",sd1hat,".\n")
y1hat=dnorm(z,theta1hat,sd1hat)
lines(z,y1hat,lty=4)