# 1
?chisq.test

chi.res<-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

chi.res$observed-chi.res$expected
# [1] -4.75 10.25  3.25 -8.75
chi.res$stdres
# [1] -1.4281275  3.0817487  0.9771398 -2.6307611

#2
chisq.test(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
exp.p<-c(1200, 200, 650, 200)

chisq.test(c(41, 5, 30, 2), p=exp.p/sum(exp.p))
# 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, df=3, lower.tail = F)
# [1] 7.814728

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

qchisq(0.05, df=8, lower.tail = F)
# [1] 15.50731

qchisq(0.01, df=8, lower.tail = F)
# [1] 20.09024