homework4.2

Homework4_2.jl

# Author: Sen Mu

# to install Distributions.jl, please julia>Pkg.add("Distributions")
using Compat, Random, Distributions

# Generate seed of random numbers
Random.seed!(241)

# create a uniform distribution (0,1)
d = Uniform(0, 1)

function f(sample_size)
    deviates = []
    for i=1:11
        # generate deviates
        x = rand(d, sample_size)
        x_mean = mean(x)
        push!(deviates, x_mean)
    end

    E_x = mean(deviates)
    Var_x = var(deviates)
    sigma = sqrt(Var_x)
    Ur = 2.23*(sigma/sqrt(11))
    lower_bound = E_x-Ur
    upper_bound = E_x+Ur
    println("Sample size = $(sample_size)")
    println("Mean:$(E_x), Deviation$(sigma)")
    println("Confidence Interval 95%:($(lower_bound), $(upper_bound))\n")
end

# different sample sizes
sample_size = [10, 100, 1000, 10000, 100000, 1000000]

# experiment with 6 different sample_sizes
for n in sample_size
    f(n)
end