# 
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

m = 2 
sigma = 1.5
m_over_sigma = m/(sigma^2)

x = seq( -4, +4, length.out=100 )
y = x

z = outer( exp(m_over_sigma * x), exp(m_over_sigma * y), FUN="+" )

gamma = 4

#postscript("../../WriteUp/Graphics/Chapter2/prob_2.2.18.eps", onefile=FALSE, horizontal=FALSE)

contour(x,y,z, levels=c(gamma), xlab="X", ylab="Y", col="black")

lb_lim = ((sigma^2)/m)*log(gamma)

segments( x[1], lb_lim, lb_lim, lb_lim, col="green" )
segments( lb_lim, x[1], lb_lim, lb_lim, col="green" )

ub_lim = ((sigma^2)/m)*log(gamma/2.)

segments( x[1], ub_lim, ub_lim, ub_lim, col="red" )
segments( ub_lim, x[1], ub_lim, ub_lim, col="red" )

#dev.off()