{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R에서의 확률분포\n",
    "d를 붙이면 확률밀도함수(probability density function)\n",
    "\n",
    "p를 붙이면 누적밀도함수(cumulation density function)\n",
    "\n",
    "q를 붙이면 분위수 함수\n",
    "\n",
    "r를 붙이면 난수를 생성함"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 정규분포(Normal Distribution)\n",
    "#####dnorm(0, mean=0, sd=1)  # N(0,1)의 0에서의 밀도 함수값\n",
    "#####pnorm(0, mean=0, sd=1)  # N(0,1)의 0까지의 누적밀도 함수값\n",
    "#####qnorm(0.5, mean=0, sd=1)  # N(0,1)의 50% 분위수 값\n",
    "#####rnorm(5, mean=0, sd=1)   # N(0,1)를 따르는 난수 5개 발생"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.398942280401433"
      ],
      "text/latex": [
       "0.398942280401433"
      ],
      "text/markdown": [
       "0.398942280401433"
      ],
      "text/plain": [
       "[1] 0.3989423"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "0.5"
      ],
      "text/latex": [
       "0.5"
      ],
      "text/markdown": [
       "0.5"
      ],
      "text/plain": [
       "[1] 0.5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "0"
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      "text/latex": [
       "0"
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      "text/markdown": [
       "0"
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      "text/plain": [
       "[1] 0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>-0.602637636895993</li>\n",
       "\t<li>-0.659182997253518</li>\n",
       "\t<li>-1.59759087550114</li>\n",
       "\t<li>0.816145418829405</li>\n",
       "\t<li>-0.802318274262988</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -0.602637636895993\n",
       "\\item -0.659182997253518\n",
       "\\item -1.59759087550114\n",
       "\\item 0.816145418829405\n",
       "\\item -0.802318274262988\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -0.602637636895993\n",
       "2. -0.659182997253518\n",
       "3. -1.59759087550114\n",
       "4. 0.816145418829405\n",
       "5. -0.802318274262988\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] -0.6026376 -0.6591830 -1.5975909  0.8161454 -0.8023183"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dnorm(0, mean=0, sd=1)  \n",
    "pnorm(0, mean=0, sd=1)  \n",
    "qnorm(0.5, mean=0, sd=1)\n",
    "rnorm(5, mean=0, sd=1)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(jupyter.plot_mimetypes = 'image/png')\n",
    "x=rnorm(10000, mean=0, sd=1)\n",
    "plot(density(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###chi-square(Chi-square Distribution)\n",
    "##### 자유도(df)가 커질 수록 정규분포에 가까워 진다.\n",
    "#### ncp(non-centrality parameter)는 선택값이다.\n",
    "#####dchisq(0, df=1) # chisq(0,1)의 0에서의 밀도 함수값\n",
    "#####pchisq(0, df=1) # chisq(0,1)의 0까지의 누적밀도 함수값\n",
    "#####qchisq(0.5, df=1) #chisq(0,1)의 50% 분위수 값\n",
    "#####rchisq(5, df=1) # N(0,1)를 따르는 난수 5개 발생"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "0"
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      "text/plain": [
       "[1] 0"
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     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "0"
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       "[1] 0"
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     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "9.34181776559197"
      ],
      "text/latex": [
       "9.34181776559197"
      ],
      "text/markdown": [
       "9.34181776559197"
      ],
      "text/plain": [
       "[1] 9.341818"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>20.1263452380664</li>\n",
       "\t<li>11.2605732317928</li>\n",
       "\t<li>14.0385219630656</li>\n",
       "\t<li>8.72324917985907</li>\n",
       "\t<li>11.9376260514098</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 20.1263452380664\n",
       "\\item 11.2605732317928\n",
       "\\item 14.0385219630656\n",
       "\\item 8.72324917985907\n",
       "\\item 11.9376260514098\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 20.1263452380664\n",
       "2. 11.2605732317928\n",
       "3. 14.0385219630656\n",
       "4. 8.72324917985907\n",
       "5. 11.9376260514098\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 20.126345 11.260573 14.038522  8.723249 11.937626"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dchisq(0, df=10)\n",
    "pchisq(0, df=10)\n",
    "qchisq(0.5, df=10)\n",
    "rchisq(5, df=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=rchisq(10000, df=10)\n",
    "sx=(x-mean(x))/(sd(x)/sqrt(10000))\n",
    "plot(density(sx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###확률(Probability)은 불확실성 속에서 이떤 사건이 일어날 가능성이 어는 정도인지를 수치화\n",
    "#####표본공간(sample space)는 통계적 실험에서 모든 가능한 실험 결과들의 집합이며, 사상(Event)는 표본 공간의 부분집합으로 관심이 있는 실험결과들의 집합임.\n",
    "##### 사상(Event) A, B에 대하여\n",
    "##### A∪ B : 합사상, A ∩ B 곱사상, Ac를 A의 여사상, A ∩ B = φ인 경우 서로 배반(disjoint)인 사상이라 한다.\n",
    "#####표본공간의 모든 원소가 일어날 가능성이 모두 같은 경우 사상 A가 일어날 확률 P(A)는\n",
    "P(A) = 사상 A에 속하는 원소의 갯수/표본공간의 전체 원소의 갯수\n",
    "#####P( A∪ B) = P(A)+P(B) - P(A ∩ B)\n",
    "#####P(Ac) = 1-P(A)\n",
    "#####P(A1∪ A2 ∪ A3 ∪ ... An) = P(A1)+P(A2)+P(A3) ... P(An) 각 사상이 배반일 경우\n",
    "#####A ⊂ B 이면 P(A) ≤ P(B)\n",
    "#### 조건부 확률 P(B|A)=P(A ∩ B)/P(A)는 곱셈정리에 의하여 P(A ∩ B) = P(B|A)*P(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(jupyter.plot_mimetypes = 'image/png')\n",
    "x=c(6,2,4,8,10) # 5 persons working years\n",
    "mean(x) # mean\n",
    "sum((x-mean(x))^2)/length(x) # variance σ2\n",
    "hist(x)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.1.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}