# 
# 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.
# 
#-----

m1 = 1
sigma1 = 1./2
N = 3

erfc = function(x) { return( 1 - pnorm(x) ) } 

gamma = seq( from=-40, to=40, length.out=200 )

#
# Part (1): 
#
P_F = erfc( gamma * sigma1 / ( sqrt(N) * m1 ) )
P_D = erfc( gamma * sigma1 / ( sqrt(N) * m1 ) - sqrt( N ) * m1 / sigma1 )

#postscript("../../WriteUp/Graphics/Chapter2/prob_2.2.20_part_1.eps", onefile=FALSE, horizontal=FALSE)

plot( P_F, P_D, col="black", type="l", xlim=c(0,1), ylim=c(0,1) )
lines( gamma, gamma, col="gray", type="l" )

#dev.off()

#
# Part (2):
#

sigma_n = 1
sigma_s = 2
N = 3

gamma = seq( from=-60, to=40, length.out=200 )

gamma_star_F = ( 2*(sigma_s^2 + sigma_n^2)/sigma_s^2 ) * gamma
P_F = ( 1 - pchisq( gamma_star_F, N ) )

gamma_star_D = ( 2*sigma_n^2/sigma_s^2 ) * gamma
P_D = ( 1 - pchisq( gamma_star_D, N ) )

#postscript("../../WriteUp/Graphics/Chapter2/prob_2.2.20_part_2.eps", onefile=FALSE, horizontal=FALSE)

plot( P_F, P_D, col="black", type="l", xlim=c(0,1), ylim=c(0,1) )
lines( gamma, gamma, col="gray", type="l")

#dev.off()