Central Limit Theorem

모집단 분포: Uniform

pop.vec = seq(from=0, to=1, length.out=20)
hist(pop.vec)

sample.mat = NULL
sample_mean.vec = NULL
for (i in 1:10){
  sample = runif(20,min=0,max=1)
  sample.mat = cbind(sample.mat, sample)
  sample_mean.vec = c(sample_mean.vec,mean(sample))
}

표본 분포

par(mfrow=c(3,3))
for (i in 1:9) hist(sample.mat[,i])

\(\LARGE \bar{X}\)의 분포

n = 20, 시행횟수 = 10

par(mfrow=c(1,1))
hist(sample_mean.vec)

sample.mat = NULL
sample_mean.vec = NULL
for (i in 1:50){
  sample = runif(20,min=0,max=1)
  sample.mat = cbind(sample.mat, sample)
  sample_mean.vec = c(sample_mean.vec,mean(sample))
}

n = 20, 시행횟수 = 50

hist(sample_mean.vec)

sample.mat = NULL
sample_mean.vec = NULL
for (i in 1:1000){
  sample = runif(20,min=0,max=1)
  sample.mat = cbind(sample.mat, sample)
  sample_mean.vec = c(sample_mean.vec,mean(sample))
}

n = 20, 시행횟수 = 1000

hist(sample_mean.vec)

모집단 분포: 표준정규분포

# pop.vec = seq(from=0, to=1, length.out=20)
# hist(pop.vec)

sample.mat = NULL
sample_mean.vec = NULL
for (i in 1:10){
  sample = rnorm(20,mean=0,sd=1)
  sample.mat = cbind(sample.mat, sample)
  sample_mean.vec = c(sample_mean.vec,mean(sample))
}

표본 분포

par(mfrow=c(3,3))
for (i in 1:9) hist(sample.mat[,i])

\(\LARGE \bar{X}\)의 분포

n = 20, 시행횟수 = 10

par(mfrow=c(1,1))
hist(sample_mean.vec)

sample.mat = NULL
sample_mean.vec = NULL
for (i in 1:50){
  sample = rnorm(20,mean=0,sd=1)
  sample.mat = cbind(sample.mat, sample)
  sample_mean.vec = c(sample_mean.vec,mean(sample))
}

n = 20, 시행횟수 = 50

hist(sample_mean.vec)

sample.mat = NULL
sample_mean.vec = NULL
for (i in 1:1000){
  sample = rnorm(20,mean=0,sd=1)
  sample.mat = cbind(sample.mat, sample)
  sample_mean.vec = c(sample_mean.vec,mean(sample))
}

n = 20, 시행횟수 = 1000

hist(sample_mean.vec)