library(stats)

# Section 2; Question 1:
#
source('chap_10_sect_2_question_1_data.R')
print( dmultinom( c(0, 0, 1, 2, 3), prob=DF$Probability ) )


# Section 2; Question 2:
#
print( dmultinom( c(1, 1, 1, 1), prob=c( 9/16, 3/16, 3/16, 1/16 ) ) )


# Section 2; Question 3:
#
m = 124
s = 13.7
p1 = pnorm( (140-m)/s )
p2 = pnorm( (160-m)/s ) - p1
p3 = 1 - p2 - p1
prob = c( p1, p2, p3 )
print( prob )
print( dmultinom( c( 6, 3, 1 ), prob=prob ) )


# Section 2; Question 4:
#
m = 100
s = 16
p1 = pnorm( (90-m)/s )
p2 = pnorm( (110-m)/s ) - p1
p3 = 1 - p2 - p1
prob = c( p1, p2, p3)
print( prob )
print( dmultinom( c( 2, 4, 1 ), prob=prob ) )


# Section 2; Question 5:
#
prob = c( 2/9, 5/18, 5/18, 2/9 )
print( dmultinom( c( 0, 2, 4, 0 ), prob=prob ) )


# Section 2; Question 6:
#
source('chap_10_sect_2_question_6_data.R')
print( dmultinom( c(2, 2, 1, 0, 0), prob=DF$Probability ) )


# Section 2; Question 7:
#
n = 50
probs = c( 1, 7, 19, 37 )/64
print( n * probs[3] * ( 1 - probs[3] ) )