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Copy pathpluto_centeral_limit.jl
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pluto_centeral_limit.jl
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### A Pluto.jl notebook ###
# v0.19.45
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ 41117df0-f9f2-11ec-0eaf-bbe82f267d42
begin
using Plots
using PlutoUI
using LinearAlgebra
using Symbolics
using LaTeXStrings
nbsp = html" "
end
# ╔═╡ dbed234b-ebf7-4448-889a-8c98cacbeda9
md"""
#### Central limit theorem for binomial distribution $B(n,p)$
"""
# ╔═╡ 174c82bf-34bd-47e7-bb52-93307f29b47c
md"""
p = $(@bind p1 Slider(0.1:0.1:0.9, show_value=true, default=0.5))
$nbsp $nbsp
n = $(@bind n1 Slider(1:1800, show_value=true, default=100))
"""
# ╔═╡ 24d518cb-7088-4efb-a87b-6882fb17c5f9
begin
x1 = range(-3, 3, length = 1201);
f1 = exp.(-x1.^2/2)/sqrt(2*pi);
z2=zeros(n1+2*max(100,n1));
for l=0:n1
z2[l+max(100,n1)+1]=Float64(sqrt(n1*p1*(1-p1))*factorial(BigInt(n1))*p1^l*(1-p1)^(n1-l)/factorial(BigInt(l))/factorial(BigInt(n1-l)));
end
z1 = zeros(length(x1));
c1 = Int64((length(x1)-1)/2);
for k=1:c1
z1[c1+k]=z2[max(100,n1)+2+Int64(floor(n1*p1+(k-1)/200*sqrt(n1*p1*(1-p1))))];
z1[c1+1-k]=z2[max(100,n1)+1+Int64(floor(n1*p1-(k-1)/200*sqrt(n1*p1*(1-p1))))];
end
end
# ╔═╡ 7b34916d-8ab9-4157-a5fd-9f45fb2915ef
begin
plot(f1,
grid=false,
ylim=(0,0.45),
xticks=([201 401 601 801 1001;],[-2,-1,0,1,2]),
yticks=([0 1/sqrt(2*pi);],[0,"1/√2π"]),
xlabel=(L"x"),
ylabel=(L"y"),
edgecolor=:false,
legend=:false,
lw=2,
color=:blue)
bar!(z1,
grid=false,
edgecolor=:false,
legend=false,
lw=0,
color=:lightpink)
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
[compat]
LaTeXStrings = "~1.3.1"
Plots = "~1.38.17"
PlutoUI = "~0.7.52"
Symbolics = "~5.5.1"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
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