#
# 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.
#
#-----

save_plots = F

# Chapter 7: Section 10: Exercise 1 (e)
#
p1 = seq( from=0, to=1, length.out=100 )
E1 = 4 - 3 * p1
E2 = 2 * rep( 1, length(p1) )
E3 = 1 + 2 * p1

max_E = max( c(E1,E2,E3) )
min_E = min( c(E1,E2,E3) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_1_Part_e.eps", onefile=FALSE, horizontal=FALSE) }

plot( p1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='p_1', ylab='expectation' )
lines( p1, E2, type='l', col='red' )
lines( p1, E3, type='l', col='purple' )

abline( v=0 )
abline( v=1.0 ) 

polygon( c(0,0.5,2/3,1.0), c(1.0,2.0,2.0,1.0), col='gray' )

grid()

if( save_plots ){ dev.off() }


# Chapter 7: Section 10: Exercise 2 (a)
#
q1 = seq( from=0, to=1, length.out=100 )
E1 = 15*(1-q1)
E2 = 8*q1
E3 = 20 - 30*q1
E4 = 12 - 2*q1

max_E = max( c(E1,E2,E3,E4) )
min_E = min( c(E1,E2,E3,E4) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_2_Part_a.eps", onefile=FALSE, horizontal=FALSE) }

plot( q1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='q_1', ylab='expectation' )
lines( q1, E2, type='l', col='red' )
lines( q1, E3, type='l', col='purple' )
lines( q1, E4, type='l', col='cyan' )

abline( v=0 )
abline( v=1.0 ) 

polygon( c(0.0,2/7,1.0,1.0), c(25,12-4/7,10,25), col='gray' )

grid()

if( save_plots ){ dev.off() }


# Chapter 7: Section 10: Exercise 2 (b)
#
p1 = seq( from=0, to=1, length.out=100 )
E1 = -2 + p1
E2 = 1 - 3 * p1
E3 = rep( 0, length(p1) )
E4 = 2 - 5 * p1
E5 = 5 - 9 * p1

max_E = max( c(E1,E2,E3,E4,E5) )
min_E = min( c(E1,E2,E3,E4,E5) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_2_Part_b.eps", onefile=FALSE, horizontal=FALSE) }

plot( p1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='p_1', ylab='expectation' )
lines( p1, E2, type='l', col='red' )
lines( p1, E3, type='l', col='purple' )
lines( p1, E4, type='l', col='cyan' )
lines( p1, E5, type='l', col='black' )

abline( v=0 )
abline( v=1.0 ) 

polygon( c(0,0,2/3,3/4,1,1), c(-5,-2,-4/3,-7/4,-4,-5), col='gray' )

grid()

if( save_plots ){ dev.off() }



# Chapter 7: Section 10: Exercise 2 (c)
#
p1 = seq( from=0, to=1, length.out=100 )
E1 = -6 + 11 * p1 
E2 = - p1 
E3 = 8 - 10 * p1
E4 = -9 + 17 * p1

max_E = max( c(E1,E2,E3,E4) )
min_E = min( c(E1,E2,E3,E4) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_2_Part_c.eps", onefile=FALSE, horizontal=FALSE) }

plot( p1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='p_1', ylab='expectation' )
lines( p1, E2, type='l', col='red' )
lines( p1, E3, type='l', col='purple' )
lines( p1, E4, type='l', col='black' )

abline( v=0 )
abline( v=1.0 ) 

polygon( c(0,0,1/2,8/9,1,1), c(-10,-9,-1/2,-8/9,-2,-10), col='gray' )

grid()

if( save_plots ){ dev.off() }


# Chapter 7: Section 10: Exercise 3
#
p1 = seq( from=0, to=1, length.out=100 )
E1 = 3 - 2 * p1 
E2 = rep( 2, length(p1) ) 
E3 = 1 + 2 * p1

max_E = max( c(E1,E2,E3) )
min_E = min( c(E1,E2,E3) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_3.eps", onefile=FALSE, horizontal=FALSE) }

plot( p1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='p_1', ylab='expectation' )
lines( p1, E2, type='l', col='red' )
lines( p1, E3, type='l', col='purple' )

abline( v=0 )
abline( v=1.0 ) 

polygon( c(0,0,0.5,1,1), c(0,1,2.0,1.0,0), col='gray' )

grid()

if( save_plots ){ dev.off() }



# Chapter 7: Section 10: Exercise 4
#
q1 = seq( from=0, to=1, length.out=100 )
E1 = -7 + 20 * q1
E2 = 8 - 5 * q1
E3 = 14 - 15 * q1
E4 = -1 + 10 * q1 

max_E = max( c(E1,E2,E3,E4) )
min_E = min( c(E1,E2,E3,E4) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_4.eps", onefile=FALSE, horizontal=FALSE) }

plot( q1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='q_1', ylab='expectation' )
lines( q1, E2, type='l', col='red' )
lines( q1, E3, type='l', col='purple' )
lines( q1, E4, type='l', col='black' )

abline( v=0 )
abline( v=1.0 ) 

polygon( c(0,0,0.6,1,1), c(15,14,5,13,15), col='gray' )

grid()

if( save_plots ){ dev.off() }


# Chapter 7: Section 10: Exercise 5
#
q1 = seq( from=0, to=1, length.out=100 )
E1 = 1 - 2 * q1
E2 = -2 + 4 * q1
E3 = 3 - 6 * q1
E4 = -4 + 8 * q1 

max_E = max( c(E1,E2,E3,E4) )
min_E = min( c(E1,E2,E3,E4) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_5.eps", onefile=FALSE, horizontal=FALSE) }

plot( q1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='q_1', ylab='expectation' )
lines( q1, E2, type='l', col='red' )
lines( q1, E3, type='l', col='purple' )
lines( q1, E4, type='l', col='purple' )

abline( v=0 )
abline( v=1.0 ) 

#polygon( c(0,0,0.5,1.0,1.0), c(1.0,-1.0,-1.5,0.0,1.0), col='gray' )

grid()

if( save_plots ){ dev.off() }



# Chapter 7: Section 10: Exercise 9 Part (c)
#

q1 = seq( from=0, to=1, length.out=100 )
E1 = -3 + 3 * q1
E2 = -1 - q1
E3 = -3 + q1 

max_E = max( c(E1,E2,E3) )
min_E = min( c(E1,E2,E3) ) 

if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/section_10_exercise_9_Part_c.eps", onefile=FALSE, horizontal=FALSE) }

plot( q1, E1, type='l', col='blue', xlim=c(-0.1,+1.1), ylim=c(min_E,max_E), xlab='q_1', ylab='expectation' )
lines( q1, E2, type='l', col='red' )
lines( q1, E3, type='l', col='purple' )

abline( v=0 )
abline( v=1.0 ) 

polygon( c(0,0,0.5,1.0,1.0), c(1.0,-1.0,-1.5,0.0,1.0), col='gray' )

grid()

if( save_plots ){ dev.off() }