#====================
# Figure 14.5.R.
# R script to draw a
# normal density curve.
#====================
mu=10
sig=sqrt(20/12)
y=(16-4)*(0:100)/100+4
pdf=exp(-(y-mu)^2/(2*sig^2))/sqrt(2*pi*sig*sig)
plot(y,pdf,type="l",ylab="density")
x0=mu
y0=0
x1=mu
y1=1/sqrt(2*pi*sig*sig)
segments(x0,y0,x1,y1,lty=2)
A=1/(2*sig*sig)
B=mu/(sig*sig)
a=4*A*A
b=-4*A*B
c=B*B-2*A
Y1=(-b+sqrt(b*b-4*a*c))/(2*a)
FY1=exp(-(Y1-mu)^2/(2*sig*sig))/sqrt(2*pi*sig*sig)
x0=mu
y0=FY1
x1=Y1
y1=FY1
segments(x0,y0,x1,y1,lty=2)
text(10.4,0,expression(mu),cex=1.5)
text(10.7,FY1-.01,expression(sigma),cex=1.5)