Practica 6 (nueva) - Ejercicio 8.ipynb

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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "![image.png](attachment:image.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a ) i ) Media:**\n",
    "\n",
    "Sumar una constante a **cada valor de la muestra** es como sumarle una constante **al promedio de la muestra**:\n",
    "\n",
    "$$\\bar X = \\frac {\\sum_{i=1}^n X_i} n $$\n",
    "\n",
    "Si sumo constante $c$:\n",
    "\n",
    "$$\\bar Y = \\frac {\\sum_{i=1}^n X_i + c} n =$$\n",
    "\n",
    "Saco $c$ afuera $n$ veces\n",
    "\n",
    "$$= \\frac {n . c + \\sum_{i=1}^n X_i} n$$\n",
    "\n",
    "$$= c + \\frac {\\sum_{i=1}^n X_i} n$$\n",
    "\n",
    "$$= c + \\bar X$$\n",
    "\n",
    "Por lo que:\n",
    "\n",
    "| Respuesta |\n",
    "|---|\n",
    "| $$\\huge Y_i = X_i + c \\implies \\bar Y = \\bar X + c$$ |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mediana:**\n",
    "\n",
    "Con la mediana es igual, pero más simple:\n",
    "\n",
    "* Si tengo una muestra de n elementos, \n",
    "  \n",
    "  y sumo $c$ a cada uno de los elementos\n",
    "  \n",
    "  desplazo cada uno de los elementos en la magnitud y sentido de $c$,\n",
    "  \n",
    "  por lo que el elemento ***del medio*** de la muestra (ordenada) antes de sumarle $c$\n",
    "  \n",
    "  seguirá estando en su posición relativa con respecto a todos los otros elementos,\n",
    "  \n",
    "  pero con magnitud modificada por $c$\n",
    "  \n",
    "  \n",
    "* Formalmente no se me ocurre, pero con números, sea la muestra ordenada:\n",
    "  \n",
    "  $$x_{(1)}, x_{(2)}, \\dots, x_{(n/2)}, \\dots, x_{(n-1)}, x_{(n)}$$\n",
    "  \n",
    "  Con $x_{(n/2)}$ la mediana de la muestra\n",
    "  \n",
    "  Si sumo $c$ a cada elemento, no cambio el órden relativo:\n",
    "  \n",
    "  $$x_{(1)}+c, x_{(2)}+c, \\dots, x_{(n/2)}+c, \\dots, x_{(n-1)}+c, x_{(n)}+c$$\n",
    "  \n",
    "  Con lo que se observa que la mediana es ahora: $x_{(n/2)}+c$\n",
    "  \n",
    "Por lo tanto:\n",
    "\n",
    "| Respuesta |\n",
    "|---|\n",
    "| $$\\huge Y_i = X_i + c \\implies \\tilde Y = \\tilde X + c$$ |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ii )** Con el producto de c es lo mismo, pero en vez de desplazar el rango, lo \"estira/comprime\"\n",
    "\n",
    "La demo es igual.\n",
    "\n",
    "\n",
    "| Respuesta |\n",
    "|---|\n",
    "| $$\\huge Y_i = c X_i \\implies \\bar Y = c \\bar X$$ |\n",
    "\n",
    "| Respuesta |\n",
    "|---|\n",
    "| $$\\huge Y_i = c X_i \\implies \\tilde Y = c \\tilde X$$ |"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**i )** \n",
    "\n",
    "$$S_X^2 = \\frac 1 {n-1} \\sum_{i=1}^n ( X_i - \\bar X )^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$S_Y^2 = \\frac 1 {n-1} \\sum_{i=1}^n ( Y_i - \\bar Y )^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $Y_i = X_i + c$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$S_Y^2 = \\frac 1 {n-1} \\sum_{i=1}^n ( X_i + c - (\\bar X + c) )^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$= \\frac 1 {n-1} \\sum_{i=1}^n ( X_i - \\bar X + c - c )^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$= \\frac 1 {n-1} \\sum_{i=1}^n ( X_i - \\bar X)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">| Que es lo mismo que |\n",
    ">|---|\n",
    ">|$$\\huge S_Y^2 = S_X^2$$|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ii )**\n",
    "\n",
    "$$S_Y^2 = \\frac 1 {n-1} \\sum_{i=1}^n ( Y_i - \\bar Y )^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $Y_i = c X_i$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$S_Y^2 = \\frac 1 {n-1} \\sum_{i=1}^n ( c X_i - \\bar c X_i )^2$$\n",
    "\n",
    "$$= \\frac 1 {n-1} \\sum_{i=1}^n ( c (X_i - \\bar X_i ))^2$$\n",
    "\n",
    "$$= \\frac 1 {n-1} \\sum_{i=1}^n c^2 (X_i - \\bar X_i )^2$$\n",
    "\n",
    "$$= \\frac 1 {n-1} c^2 \\sum_{i=1}^n  (X_i - \\bar X_i )^2$$\n",
    "\n",
    "$$= c^2 \\frac 1 {n-1}  \\sum_{i=1}^n  (X_i - \\bar X_i )^2$$\n",
    "\n",
    ">| Que es lo mismo que |\n",
    ">|---|\n",
    ">|$$\\huge  S_Y^2 = c^2 S_X^2$$|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**iii )**\n",
    "\n",
    "$$S_X^2 = \\frac 1 {n-1} \\sum_{i=1}^n X_i^2 - \\frac n {n-1} \\bar X^2$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sé que \n",
    "\n",
    "$$S_X^2 = \\frac 1 {n-1} \\sum_{i=1}^n ( X_i - \\bar X )^2$$\n",
    "\n",
    "Abro el cuadrado\n",
    "\n",
    "$$= \\frac 1 {n-1} \\sum_{i=1}^n ( X_i - 2 X_i \\bar X^2 + \\bar X^2 )$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Separo la suma\n",
    "\n",
    "$$= \\left(  \\frac 1 {n-1} \\sum_{i=1}^n X_i^2 \\right) - \\left( \\frac 1 {n-1} \\sum_{i=1}^n 2 X_i \\bar X \\right) + \\left( \\frac 1 {n-1} \\sum_{i=1}^n \\bar X^2 \\right) $$\n",
    "\n",
    "Donde el promedio **no** depende de i:\n",
    "\n",
    "> $$S_X^2 = \\left(  \\frac 1 {n-1} \\sum_{i=1}^n X_i^2 \\right) - \\left( \\frac 1 {n-1} \\sum_{i=1}^n 2 X_i \\bar X \\right) + \\left( \\frac n {n-1} \\bar X^2 \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Donde el primer término corresponde al primer término a probar.\n",
    "\n",
    "Y el segundo:\n",
    "\n",
    "$$\\frac 1 {n-1} \\sum_{i=1}^n 2 X_i \\bar X =$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$= 2 \\bar X \\frac 1 {n-1} \\sum_{i=1}^n X_i$$\n",
    "\n",
    "Divido y multiplico por $n$ para que aparezca **otro** promedio $\\bar X$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$= 2 \\bar X \\frac 1 {n-1} n \\frac {\\sum_{i=1}^n X_i} n$$\n",
    "\n",
    "$$= 2 \\bar X \\frac 1 {n-1} n \\bar X $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$=  2 \\frac {n} {n-1} \\bar X^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reemplazando en la suma de antes:\n",
    "\n",
    "> $$S_X^2 = \\left(  \\frac 1 {n-1} \\sum_{i=1}^n X_i^2 \\right) - \\left( 2 \\frac {n} {n-1} \\bar X^2 \\right) + \\left( \\frac n {n-1} \\bar X^2 \\right) $$\n",
    "\n",
    ">| Con lo que obtenemos la relación a probar |\n",
    ">|---|\n",
    ">|$$\\huge S_X^2 = \\left(  \\frac 1 {n-1} \\sum_{i=1}^n X_i^2 \\right) - \\left( \\frac {n} {n-1} \\bar X^2 \\right) $$|"
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    "---\n",
    "\n",
    "$$Fin$$\n",
    "\n",
    "---"
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