# Exercise 10.1
set.seed(12321)

p <- rep(NA, 1000)

for(i in 1:1000) p[i] <- mean(rbinom(100, 1, 0.2))

mean(p)
sd(p)

hist(p)

# Exercise 10.2

set.seed(12321)

binary.l <- list()

for(i in 1:1000) binary.l[[i]] <- rbinom(100, 1, 0.2)

p2 <- sapply(binary.l, mean)

tab2 <- lapply(binary.l, table)
test2 <- lapply(tab2, chisq.test, correct = FALSE, p = c(0.8, 0.2))
pvalue2 <- sapply(test2, "[[", "p.value")
mean(pvalue2 < 0.05)

# Exercise 10.3

library(parallel)

set.seed(12321)
seed.l <- sample(1:999999, 1000)

FUN3 <- function(seed) {
	set.seed(seed)
	x <- rbinom(100, 1, 0.2)
	tab <- table(x)
	test <- chisq.test(tab, correct = FALSE, p = c(0.8, 0.2))
	test[["p.value"]]
}

cl <- makeCluster(rep("localhost", 2), type = "PSOCK")
output.l <- parLapply(cl, seed.l, FUN3)
stopCluster(cl)
pvalue3 <- do.call(c, output.l)
mean(pvalue3 < 0.05)

# Homework 10

# 1.1

set.seed(12321)
sds <- rep(NA, 1000)
for(i in 1:1000) sds[i] <- sd(rnorm(100, 0, 1))
mean(sds) - 1

# 1.2

set.seed(12321)
dat.l <- list()
for(i in 1:1000) dat.l[[i]] <- rnorm(100, 0, 1)
sds2 <- sapply(dat.l, sd)
mean(sds2) - 1

# 1.3

set.seed(12321)
seed.l <- sample(1:999999, 1000)

FUN13 <- function(seed) {
	set.seed(seed)
	x <- rnorm(100, 0, 1)
	sd(x)
}

cl <- makeCluster(rep("localhost", 2), type = "PSOCK")
output.l <- parLapply(cl, seed.l, FUN13)
stopCluster(cl)
sds3 <- do.call(c, output.l)
mean(sds3) - 1

# 2.1

set.seed(12321)
cover1 <- rep(NA, 1000) 
n <- 100

for(i in 1:1000) {
	x <- rnorm(n, 0, 1)
	y <- 0.5*x + rnorm(n, 0, 0.8)
	cf <- confint(lm(y ~ x))
	cover1[i] <- (cf[2, 1] < 0.5) & (0.5 < cf[2, 2])
}
mean(cover1)

# 2.2

set.seed(12321)

dat.l <- list()
for(i in 1:1000) {
	x <- rnorm(n, 0, 1)
	y <- 0.5*x + rnorm(n, 0, 0.8)
	dat.l[[i]] <- data.frame(x, y)
}

out.l <- lapply(dat.l, lm, formula = y ~ x)
cf <- t(sapply(out.l, confint))
cover2 <- (cf[,2] < 0.5) & (0.5 < cf[,4])
mean(cover2)

# 2.3

set.seed(12321)
seed.l <- sample(1:999999, 1000)

FUN23 <- function(seed) {
	set.seed(seed)
	n <- 100
	x <- rnorm(n, 0, 1)
	y <- 0.5*x + rnorm(n, 0, 0.8)
	cf <- confint(lm(y ~ x))
	(cf[2, 1] < 0.5) & (0.5 < cf[2, 2])
}

cl <- makeCluster(rep("localhost", 2), type = "PSOCK")
output.l <- parLapply(cl, seed.l, FUN23)
stopCluster(cl)
cover3 <- do.call(c, output.l)
mean(cover3)