#1
chisq.test(x=c(10, 25, 18, 6), 
           p=rep(1/4, 4))
# Chi-squared test for given
# 	probabilities
# 
# data:  c(10, 25, 18, 6)
# X-squared = 14.559, df = 3, p-value
# = 0.002235


test.res<-chisq.test(x=c(10, 25, 18, 6), 
           p=rep(1/4, 4))
test.res$observed-test.res$expected
# [1] -4.75 10.25  3.25 -8.75

#2
chisq.test(x=c(125, 60,50, 12),
           p=c(9/16, 3/16,3/16,1/16))
# 	Chi-squared test for given
# 	probabilities
# 
# data:  c(125, 60, 50, 12)
# X-squared = 6.5025, df = 3, p-value
# = 0.08956

#3
sum(c(1200 , 200, 650, 200))
# [1] 2250

chisq.test(x=c(41, 5, 30,2), 
           p=c(1200/2250 , 200/2250, 650
               /2250, 200/2250))
# 	Chi-squared test for given
# 	probabilities
# 
# data:  c(41, 5, 30, 2)
# X-squared = 6.5322, df = 3, p-value
# = 0.0884

#4
pchisq(5.04, df=3, lower.tail = F)
# [1] 0.1688915

#5
qchisq(0.05, 3, lower.tail = F)
# [1] 7.814728

qchisq(0.01, 3, lower.tail = F)
# [1] 11.34487

#E
chisq.test(c(19,61, 25), 
           p=c(1/4,2/4, 1/4))
# X-squared = 3.4381, df = 2, p-value
# = 0.1792