"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# üldised vahendid\n",
"import numpy as np\n",
"from numpy import linspace, arange, exp, sin, cos, log, sqrt, pi, fix\n",
"from numpy.random import randn, uniform, rand\n",
"from matplotlib.pyplot import *\n",
"from matplotlib import rcParams"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"rcParams['figure.dpi'] = 100\n",
"rcParams['lines.markersize'] = 4\n",
"rcParams['lines.markeredgewidth'] = 1\n",
"rcParams['font.size'] = 12\n",
"rcParams['axes.prop_cycle'] = cycler('color', 'bgr')\n",
"\n",
"def harrow(x, y, p): # horis. nool pikkusega p alates punktist (x,y)\n",
" annotate('', xy=(x + p, y), xytext=(x, y),\n",
" arrowprops=dict(arrowstyle='-|>', color='black') )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Jaotusfunktsioon, keskväärtus ja dispersioon"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pidevat juhuslikku suurust $X$ iseloomustab *tõenäosustihedusfunktsioon* $f_X(x)$, kus $f_X(x)dx$ annab tõenäosuse, et järjekordsel katsel omandab $X$ väärtuse vahemikus $x\\ldots x+dx$: $$P(x\\leq X\\leq x+dx)=f_X(x)\\,dx.$$ *Kumulatiivne jaotusfunktsioon* $F_X(x)$ annab tõenäosuse, et saadud $X$-i väärtus on väiksem kui $x$: $$P(X\\leq x)=F_X(x)=\\int_{-\\infty}^x f_X(u)\\,du.$$ Ilmselt $$P(a\\leq X\\leq b)=\\int_a^b f_X(x)\\,dx=F_X(b)-F_X(a).$$ Kuna funktsioonid $f_X(x)$ ja $F_X(x)$ väljendavad tõenäosuseid, siis ilmselt $$\\int_{-\\infty}^\\infty f_X(x)\\,dx=1,\\quad F_X(-\\infty)=0,\\quad F_X(\\infty)=1.$$\n",
"\n",
"Jaotusfunktsiooni võib karakteriseerida mõningate skalaarsete väärtustega, mida nimetatakse [momentideks](https://en.wikipedia.org/wiki/Moment_%28mathematics%29). Esimest järku moment on [keskväärtus](https://en.wikipedia.org/wiki/Expected_value) (ehk ooteväärtus):\n",
"$$\\mu=\\expval(X)=\\int_{-\\infty}^\\infty x\\,f_X(x)\\,dx.$$ Teist järku tsentraalmoment on [dispersioon](https://en.wikipedia.org/wiki/Variance): $$\\sigma^2=\\dispers(X)=\\int_{-\\infty}^\\infty (x-\\mu)^2f_X(x)\\,dx.$$ Viimane iseloomustab juhusliku suuruse varieeruvust. $\\dispers(X)$ asemel võib anda ka [standardhälbe](https://en.wikipedia.org/wiki/Standard_deviation) $\\sigma=\\sqrt{\\dispers(X)}$, mis on $X$-ga samas skaalas ja seega otseselt võrreldav $\\mu$-ga.\n",
"\n",
"Näiteks [normaaljaotuse](https://en.wikipedia.org/wiki/Normal_distribution) tihedusfunktsioon otseselt avaldub $\\mu$ ja $\\sigma$ kaudu: $$f_X(x)=\\frac{1}{\\sqrt{2\\pi}\\sigma}\\exp\\left[-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right].$$ Siin vahe $x-\\mu$ tsentreerib jaotuse kohal $x=\\mu$ ja jagamine $\\sigma$-ga tingib vajaliku mastaabimuutuse.\n",
"\n",
"Normaaljaotuse kumulatiivne jaotusfunktsioon $F_X(x)$ ei avaldu elementaarfunktsioonides ja on aluseks erifunktsioonile $\\erf$. [Suur hulk](https://docs.scipy.org/doc/scipy/reference/special.html) selliseid (vektoriseeritud) erifunktsioone on realiseeritud moodulis `scipy.special` (veafunktsioon `erf` ja [Gammafunktsioon](https://en.wikipedia.org/wiki/Gamma_function) `gamma` on siiski nii tuntud, et need saaks vajadusel ka moodulist `math`)."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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