problem7_7.ipynb

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       "15-element Array{Float64,1}:\n",
       " 10.5\n",
       " 10.4\n",
       " 10.6\n",
       " 11.9\n",
       " 11.3\n",
       " 11.8\n",
       " 11.7\n",
       " 12.6\n",
       " 10.9\n",
       " 11.1\n",
       " 13.0\n",
       " 11.2\n",
       " 13.4\n",
       " 10.8\n",
       " 11.1"
      ]
     },
     "execution_count": 3,
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   "source": [
    "x = [10.5,\n",
    "10.4,\n",
    "10.6,\n",
    "11.9,\n",
    "11.3,\n",
    "11.8,\n",
    "11.7,\n",
    "12.6,\n",
    "10.9,\n",
    "11.1,\n",
    "13.0,\n",
    "11.2,\n",
    "13.4,\n",
    "10.8,\n",
    "11.1\n",
    "]"
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  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "ErrorException",
     "evalue": "No user recipe defined for Pair{String,String}",
     "output_type": "error",
     "traceback": [
      "No user recipe defined for Pair{String,String}",
      "",
      "Stacktrace:",
      " [1] error(::String) at .\\error.jl:33",
      " [2] convertToAnyVector(::Pair{String,String}, ::Dict{Symbol,Any}) at C:\\Users\\KIMURA\\.julia\\packages\\Plots\\y6yik\\src\\series.jl:14",
      " [3] macro expansion at C:\\Users\\KIMURA\\.julia\\packages\\Plots\\y6yik\\src\\series.jl:139 [inlined]",
      " [4] apply_recipe(::Dict{Symbol,Any}, ::Type{Plots.SliceIt}, ::Array{Float64,1}, ::Pair{String,String}, ::Nothing) at C:\\Users\\KIMURA\\.julia\\packages\\RecipesBase\\Uz5AO\\src\\RecipesBase.jl:275",
      " [5] _process_userrecipes(::Plots.Plot{Plots.GRBackend}, ::Dict{Symbol,Any}, ::Tuple{Array{Float64,1},Pair{String,String}}) at C:\\Users\\KIMURA\\.julia\\packages\\Plots\\y6yik\\src\\pipeline.jl:83",
      " [6] macro expansion at .\\logging.jl:307 [inlined]",
      " [7] _plot!(::Plots.Plot{Plots.GRBackend}, ::Dict{Symbol,Any}, ::Tuple{Array{Float64,1},Pair{String,String}}) at C:\\Users\\KIMURA\\.julia\\packages\\Plots\\y6yik\\src\\plot.jl:171",
      " [8] #plot#132(::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::Function, ::Array{Float64,1}, ::Vararg{Any,N} where N) at C:\\Users\\KIMURA\\.julia\\packages\\Plots\\y6yik\\src\\plot.jl:57",
      " [9] plot(::Array{Float64,1}, ::Pair{String,String}) at C:\\Users\\KIMURA\\.julia\\packages\\Plots\\y6yik\\src\\plot.jl:51",
      " [10] top-level scope at In[5]:2"
     ]
    }
   ],
   "source": [
    "using Plots\n"
   ]
  },
  {
   "cell_type": "code",
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   ],
   "source": [
    "histogram(x, bins=12)"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "using StatsBase"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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     "execution_count": 25,
     "metadata": {},
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   "source": [
    "y = StatsBase.mean(x)"
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   "metadata": {},
   "outputs": [
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     "execution_count": 33,
     "metadata": {},
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   ],
   "source": [
    "n = length(x)\n",
    "m_2 = sum([(x[i]-y)^2 for i in 1:n])/n\n",
    "m_3 = sum([(x[i]-y)^3 for i in 1:n])/n\n",
    "m_4 = sum([(x[i]-y)^4 for i in 1:n])/n"
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  {
   "cell_type": "code",
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    "b_1 = m_3/m_2^(3/2)"
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  {
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   "metadata": {},
   "outputs": [
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    "b_2 = m_4/m_2^2-3"
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  {
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   "metadata": {},
   "outputs": [
    {
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     "execution_count": 38,
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   "source": [
    "histogram(x, bins=12)"
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  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.166666666666668"
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     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "y = StatsBase.mean(x)"
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  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8792.596274074074"
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     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "n = length(x)\n",
    "m_2 = sum([(x[i]-y)^2 for i in 1:n])/n\n",
    "m_3 = sum([(x[i]-y)^3 for i in 1:n])/n\n",
    "m_4 = sum([(x[i]-y)^4 for i in 1:n])/n"
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  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9015930214865757"
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     "execution_count": 41,
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   "source": [
    "b_1 = m_3/m_2^(3/2)"
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  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "execution_count": 42,
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     "output_type": "execute_result"
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   "source": [
    "b_2 = m_4/m_2^2-3"
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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