File:GauStudent12345big.png

Explicit plot of the Student Distribution (aka probability density of the student t-distribution) :

\(\displaystyle y= \mathrm{Student}(n,x) \)

For the last case,

\(\displaystyle y= \mathrm{Student}(\infty,x) = \mathrm{Gau}(x)= \frac{\exp(-z^2/2)}{\sqrt\pi} \)

In general case, the Student Distribution can be expressed through the Factorial function:

\(\displaystyle \mathrm{Sturent}(n,x) = \) \(\displaystyle \frac {\ \mathrm{Factorial}\left(\frac{n-1}{2}\right)\ } {\ \sqrt{\pi n }\ \mathrm{Factorial}\left(\frac{n}{2}-1\right)} \left( 1 + \frac{~ x^2}{n}\right)^{-(n+1)/2} \)

C++ Generator

// File Student.cin should be loaded in order to compile the code below. The Latex support also should be installed.

#include <stdio.h> 
#include <math.h>
#include <stdlib.h>
//#include "ju24da.cin"

float Gau(float x){ return 1./sqrt(2*M_PI) * exp(-x*x/2); }

#include "Student.cin"

int main()
{ int n; FILE *o; o=fopen("GauStudent12345big.tex","w");
fprintf(o,"\\documentclass{standalone}\n");
fprintf(o,"\\usepackage{tikz}\n");
fprintf(o,"\\usepackage{graphicx}\n");
fprintf(o,"\\begin{document}\n");
fprintf(o,"\\scalebox{7}{\\begin{tikzpicture}\n");
fprintf(o,"\\draw [help lines] (-4,0) grid (4,4);\n");
fprintf(o,"\\draw(-4.1,0) -- (4.1,0) ;\n");
fprintf(o,"\\draw(0,0) -- (0,4.2) ;\n");
for(n=-3;n<4;n++) fprintf(o,"\\draw (%d,0) node[below] {%d};\n",n,n);
		  fprintf(o,"\\draw (%d,0) node[below] {$x$};\n",n);
for(n=1;n<4;n++) fprintf(o,"\\draw (0,%d) node[left] {0.%d};\n",n,n);
		 fprintf(o,"\\draw (0,%d) node[left] {$y ~$};\n",n);
float x,y,z;
int m;

for(n=0;n<165;n++)
{	x=-4.1+.05*n; y=10*Gau(x);
	if(n==0) fprintf(o,"\\draw[line width=.6, black] (%6.3f,%5.3f)",x,y);
	else fprintf(o," -- (%6.3f,%5.3f)",x,y);
}
fprintf(o,";\n");

m=1; z=1.;
//z=sqrt(m/(m-2.));
for(n=0;n<165;n++)
{	x=-4.1+.05*n; y=10*Student(m,x*z)*z;
	if(n==0) fprintf(o,"\\draw[line width=.4, pink] (%6.3f,%5.3f)",x,y);
	else fprintf(o," -- (%6.3f,%5.3f)",x,y);
}
fprintf(o,";\n");

m=2; z=1.;
//z=sqrt(m/(m-2.));
for(n=0;n<165;n++)
{	x=-4.1+.05*n; y=10*Student(m,x*z)*z;
	if(n==0) fprintf(o,"\\draw[line width=.4, brown] (%6.3f,%5.3f)",x,y);
	else fprintf(o," -- (%6.3f,%5.3f)",x,y);
}
fprintf(o,";\n");

m=3; z=1.;
//z=sqrt(m/(m-2.));
for(n=0;n<165;n++)
{	x=-4.1+.05*n; y=10*Student(m,x*z)*z;
	if(n==0) fprintf(o,"\\draw[line width=.6, red] (%6.3f,%5.3f)",x,y);
	else fprintf(o," -- (%6.3f,%5.3f)",x,y);
}
fprintf(o,";\n");

m=4; 
//z=sqrt(m/(m-2.));
for(n=0;n<165;n++)
{	x=-4.1+.05*n; y=10*Student(m,x*z)*z;
	if(n==0) fprintf(o,"\\draw[line width=.6, green] (%6.3f,%5.3f)",x,y);
	else fprintf(o," -- (%6.3f,%5.3f)",x,y);
}
fprintf(o,";\n");

m=5; 
//z=sqrt(m/(m-2.));
for(n=0;n<165;n++)
{	x=-4.1+.05*n; y=10*Student(m,x*z)*z;
	if(n==0) fprintf(o,"\\draw[line width=.6, blue] (%6.3f,%5.3f)",x,y);
	else fprintf(o," -- (%6.3f,%5.3f)",x,y);
}
fprintf(o,";\n");

fprintf(o,"\\end{tikzpicture}}\n");
fprintf(o,"\\end{document}\n");
fclose(o);
system("pdflatex GauStudent12345big.tex");
system("convert GauStudent12345big.pdf png8:GauStudent12345big.png");
system("open GauStudent12345big.pdf");
system("identify GauStudent12345big.png");
}

// With this code, the Latex document is generated

Latex

\documentclass{standalone}
\usepackage{tikz}
\usepackage{graphicx}
\begin{document}
\scalebox{7}{\begin{tikzpicture}
\draw [help lines] (-4,0) grid (4,4);
\draw(-4.1,0) -- (4.1,0) ;
\draw(0,0) -- (0,4.2) ;
\draw (-3,0) node[below] {-3};
\draw (-2,0) node[below] {-2};
\draw (-1,0) node[below] {-1};
\draw (0,0) node[below] {0};
\draw (1,0) node[below] {1};
\draw (2,0) node[below] {2};
\draw (3,0) node[below] {3};
\draw (4,0) node[below] {$x$};
\draw (0,1) node[left] {0.1};
\draw (0,2) node[left] {0.2};
\draw (0,3) node[left] {0.3};
\draw (0,4) node[left] {$y ~$};
\draw[line width=.6, black] (-4.100,0.001) -- (-4.050,0.001) -- (-4.000,0.001) -- (-3.950,0.002) -- (-3.900,0.002) -- (-3.850,0.002) -- (-3.800,0.003) -- (-3.750,0.004) -- (-3.700,0.004) -- (-3.650,0.005) -- (-3.600,0.006) -- (-3.550,0.007) -- (-3.500,0.009) -- (-3.450,0.010) -- (-3.400,0.012) -- (-3.350,0.015) -- (-3.300,0.017) -- (-3.250,0.020) -- (-3.200,0.024) -- (-3.150,0.028) -- (-3.100,0.033) -- (-3.050,0.038) -- (-3.000,0.044) -- (-2.950,0.051) -- (-2.900,0.060) -- (-2.850,0.069) -- (-2.800,0.079) -- (-2.750,0.091) -- (-2.700,0.104) -- (-2.650,0.119) -- (-2.600,0.136) -- (-2.550,0.154) -- (-2.500,0.175) -- (-2.450,0.198) -- (-2.400,0.224) -- (-2.350,0.252) -- (-2.300,0.283) -- (-2.250,0.317) -- (-2.200,0.355) -- (-2.150,0.396) -- (-2.100,0.440) -- (-2.050,0.488) -- (-2.000,0.540) -- (-1.950,0.596) -- (-1.900,0.656) -- (-1.850,0.721) -- (-1.800,0.790) -- (-1.750,0.863) -- (-1.700,0.940) -- (-1.650,1.023) -- (-1.600,1.109) -- (-1.550,1.200) -- (-1.500,1.295) -- (-1.450,1.394) -- (-1.400,1.497) -- (-1.350,1.604) -- (-1.300,1.714) -- (-1.250,1.826) -- (-1.200,1.942) -- (-1.150,2.059) -- (-1.100,2.179) -- (-1.050,2.299) -- (-1.000,2.420) -- (-0.950,2.541) -- (-0.900,2.661) -- (-0.850,2.780) -- (-0.800,2.897) -- (-0.750,3.011) -- (-0.700,3.123) -- (-0.650,3.230) -- (-0.600,3.332) -- (-0.550,3.429) -- (-0.500,3.521) -- (-0.450,3.605) -- (-0.400,3.683) -- (-0.350,3.752) -- (-0.300,3.814) -- (-0.250,3.867) -- (-0.200,3.910) -- (-0.150,3.945) -- (-0.100,3.970) -- (-0.050,3.984) -- ( 0.000,3.989) -- ( 0.050,3.984) -- ( 0.100,3.970) -- ( 0.150,3.945) -- ( 0.200,3.910) -- ( 0.250,3.867) -- ( 0.300,3.814) -- ( 0.350,3.752) -- ( 0.400,3.683) -- ( 0.450,3.605) -- ( 0.500,3.521) -- ( 0.550,3.429) -- ( 0.600,3.332) -- ( 0.650,3.230) -- ( 0.700,3.123) -- ( 0.750,3.011) -- ( 0.800,2.897) -- ( 0.850,2.780) -- ( 0.900,2.661) -- ( 0.950,2.541) -- ( 1.000,2.420) -- ( 1.050,2.299) -- ( 1.100,2.179) -- ( 1.150,2.059) -- ( 1.200,1.942) -- ( 1.250,1.826) -- ( 1.300,1.714) -- ( 1.350,1.604) -- ( 1.400,1.497) -- ( 1.450,1.394) -- ( 1.500,1.295) -- ( 1.550,1.200) -- ( 1.600,1.109) -- ( 1.650,1.023) -- ( 1.700,0.940) -- ( 1.750,0.863) -- ( 1.800,0.790) -- ( 1.850,0.721) -- ( 1.900,0.656) -- ( 1.950,0.596) -- ( 2.000,0.540) -- ( 2.050,0.488) -- ( 2.100,0.440) -- ( 2.150,0.396) -- ( 2.200,0.355) -- ( 2.250,0.317) -- ( 2.300,0.283) -- ( 2.350,0.252) -- ( 2.400,0.224) -- ( 2.450,0.198) -- ( 2.500,0.175) -- ( 2.550,0.154) -- ( 2.600,0.136) -- ( 2.650,0.119) -- ( 2.700,0.104) -- ( 2.750,0.091) -- ( 2.800,0.079) -- ( 2.850,0.069) -- ( 2.900,0.060) -- ( 2.950,0.051) -- ( 3.000,0.044) -- ( 3.050,0.038) -- ( 3.100,0.033) -- ( 3.150,0.028) -- ( 3.200,0.024) -- ( 3.250,0.020) -- ( 3.300,0.017) -- ( 3.350,0.015) -- ( 3.400,0.012) -- ( 3.450,0.010) -- ( 3.500,0.009) -- ( 3.550,0.007) -- ( 3.600,0.006) -- ( 3.650,0.005) -- ( 3.700,0.004) -- ( 3.750,0.004) -- ( 3.800,0.003) -- ( 3.850,0.002) -- ( 3.900,0.002) -- ( 3.950,0.002) -- ( 4.000,0.001) -- ( 4.050,0.001) -- ( 4.100,0.001);
\draw[line width=.4, pink] (-4.100,0.179) -- (-4.050,0.183) -- (-4.000,0.187) -- (-3.950,0.192) -- (-3.900,0.196) -- (-3.850,0.201) -- (-3.800,0.206) -- (-3.750,0.211) -- (-3.700,0.217) -- (-3.650,0.222) -- (-3.600,0.228) -- (-3.550,0.234) -- (-3.500,0.240) -- (-3.450,0.247) -- (-3.400,0.253) -- (-3.350,0.260) -- (-3.300,0.268) -- (-3.250,0.275) -- (-3.200,0.283) -- (-3.150,0.291) -- (-3.100,0.300) -- (-3.050,0.309) -- (-3.000,0.318) -- (-2.950,0.328) -- (-2.900,0.338) -- (-2.850,0.349) -- (-2.800,0.360) -- (-2.750,0.372) -- (-2.700,0.384) -- (-2.650,0.397) -- (-2.600,0.410) -- (-2.550,0.424) -- (-2.500,0.439) -- (-2.450,0.455) -- (-2.400,0.471) -- (-2.350,0.488) -- (-2.300,0.506) -- (-2.250,0.525) -- (-2.200,0.545) -- (-2.150,0.566) -- (-2.100,0.588) -- (-2.050,0.612) -- (-2.000,0.637) -- (-1.950,0.663) -- (-1.900,0.690) -- (-1.850,0.720) -- (-1.800,0.751) -- (-1.750,0.784) -- (-1.700,0.818) -- (-1.650,0.855) -- (-1.600,0.894) -- (-1.550,0.936) -- (-1.500,0.979) -- (-1.450,1.026) -- (-1.400,1.075) -- (-1.350,1.128) -- (-1.300,1.183) -- (-1.250,1.242) -- (-1.200,1.305) -- (-1.150,1.371) -- (-1.100,1.440) -- (-1.050,1.514) -- (-1.000,1.592) -- (-0.950,1.673) -- (-0.900,1.759) -- (-0.850,1.848) -- (-0.800,1.941) -- (-0.750,2.037) -- (-0.700,2.136) -- (-0.650,2.238) -- (-0.600,2.341) -- (-0.550,2.444) -- (-0.500,2.546) -- (-0.450,2.647) -- (-0.400,2.744) -- (-0.350,2.836) -- (-0.300,2.920) -- (-0.250,2.996) -- (-0.200,3.061) -- (-0.150,3.113) -- (-0.100,3.152) -- (-0.050,3.175) -- ( 0.000,3.183) -- ( 0.050,3.175) -- ( 0.100,3.152) -- ( 0.150,3.113) -- ( 0.200,3.061) -- ( 0.250,2.996) -- ( 0.300,2.920) -- ( 0.350,2.836) -- ( 0.400,2.744) -- ( 0.450,2.647) -- ( 0.500,2.546) -- ( 0.550,2.444) -- ( 0.600,2.341) -- ( 0.650,2.238) -- ( 0.700,2.136) -- ( 0.750,2.037) -- ( 0.800,1.941) -- ( 0.850,1.848) -- ( 0.900,1.759) -- ( 0.950,1.673) -- ( 1.000,1.592) -- ( 1.050,1.514) -- ( 1.100,1.440) -- ( 1.150,1.371) -- ( 1.200,1.305) -- ( 1.250,1.242) -- ( 1.300,1.183) -- ( 1.350,1.128) -- ( 1.400,1.075) -- ( 1.450,1.026) -- ( 1.500,0.979) -- ( 1.550,0.936) -- ( 1.600,0.894) -- ( 1.650,0.855) -- ( 1.700,0.818) -- ( 1.750,0.784) -- ( 1.800,0.751) -- ( 1.850,0.720) -- ( 1.900,0.690) -- ( 1.950,0.663) -- ( 2.000,0.637) -- ( 2.050,0.612) -- ( 2.100,0.588) -- ( 2.150,0.566) -- ( 2.200,0.545) -- ( 2.250,0.525) -- ( 2.300,0.506) -- ( 2.350,0.488) -- ( 2.400,0.471) -- ( 2.450,0.455) -- ( 2.500,0.439) -- ( 2.550,0.424) -- ( 2.600,0.410) -- ( 2.650,0.397) -- ( 2.700,0.384) -- ( 2.750,0.372) -- ( 2.800,0.360) -- ( 2.850,0.349) -- ( 2.900,0.338) -- ( 2.950,0.328) -- ( 3.000,0.318) -- ( 3.050,0.309) -- ( 3.100,0.300) -- ( 3.150,0.291) -- ( 3.200,0.283) -- ( 3.250,0.275) -- ( 3.300,0.268) -- ( 3.350,0.260) -- ( 3.400,0.253) -- ( 3.450,0.247) -- ( 3.500,0.240) -- ( 3.550,0.234) -- ( 3.600,0.228) -- ( 3.650,0.222) -- ( 3.700,0.217) -- ( 3.750,0.211) -- ( 3.800,0.206) -- ( 3.850,0.201) -- ( 3.900,0.196) -- ( 3.950,0.192) -- ( 4.000,0.187) -- ( 4.050,0.183) -- ( 4.100,0.179);
\draw[line width=.4, brown] (-4.100,0.123) -- (-4.050,0.127) -- (-4.000,0.131) -- (-3.950,0.135) -- (-3.900,0.140) -- (-3.850,0.145) -- (-3.800,0.150) -- (-3.750,0.155) -- (-3.700,0.161) -- (-3.650,0.167) -- (-3.600,0.173) -- (-3.550,0.179) -- (-3.500,0.186) -- (-3.450,0.193) -- (-3.400,0.200) -- (-3.350,0.208) -- (-3.300,0.216) -- (-3.250,0.225) -- (-3.200,0.234) -- (-3.150,0.243) -- (-3.100,0.253) -- (-3.050,0.263) -- (-3.000,0.274) -- (-2.950,0.286) -- (-2.900,0.298) -- (-2.850,0.311) -- (-2.800,0.324) -- (-2.750,0.338) -- (-2.700,0.353) -- (-2.650,0.369) -- (-2.600,0.386) -- (-2.550,0.403) -- (-2.500,0.422) -- (-2.450,0.442) -- (-2.400,0.463) -- (-2.350,0.485) -- (-2.300,0.508) -- (-2.250,0.533) -- (-2.200,0.559) -- (-2.150,0.587) -- (-2.100,0.616) -- (-2.050,0.647) -- (-2.000,0.680) -- (-1.950,0.715) -- (-1.900,0.753) -- (-1.850,0.792) -- (-1.800,0.834) -- (-1.750,0.878) -- (-1.700,0.925) -- (-1.650,0.974) -- (-1.600,1.027) -- (-1.550,1.083) -- (-1.500,1.141) -- (-1.450,1.203) -- (-1.400,1.269) -- (-1.350,1.338) -- (-1.300,1.411) -- (-1.250,1.487) -- (-1.200,1.567) -- (-1.150,1.651) -- (-1.100,1.739) -- (-1.050,1.830) -- (-1.000,1.925) -- (-0.950,2.022) -- (-0.900,2.123) -- (-0.850,2.226) -- (-0.800,2.331) -- (-0.750,2.438) -- (-0.700,2.545) -- (-0.650,2.652) -- (-0.600,2.758) -- (-0.550,2.862) -- (-0.500,2.963) -- (-0.450,3.059) -- (-0.400,3.150) -- (-0.350,3.234) -- (-0.300,3.310) -- (-0.250,3.376) -- (-0.200,3.432) -- (-0.150,3.477) -- (-0.100,3.509) -- (-0.050,3.529) -- ( 0.000,3.536) -- ( 0.050,3.529) -- ( 0.100,3.509) -- ( 0.150,3.477) -- ( 0.200,3.432) -- ( 0.250,3.376) -- ( 0.300,3.310) -- ( 0.350,3.234) -- ( 0.400,3.150) -- ( 0.450,3.059) -- ( 0.500,2.963) -- ( 0.550,2.862) -- ( 0.600,2.758) -- ( 0.650,2.652) -- ( 0.700,2.545) -- ( 0.750,2.438) -- ( 0.800,2.331) -- ( 0.850,2.226) -- ( 0.900,2.123) -- ( 0.950,2.022) -- ( 1.000,1.925) -- ( 1.050,1.830) -- ( 1.100,1.739) -- ( 1.150,1.651) -- ( 1.200,1.567) -- ( 1.250,1.487) -- ( 1.300,1.411) -- ( 1.350,1.338) -- ( 1.400,1.269) -- ( 1.450,1.203) -- ( 1.500,1.141) -- ( 1.550,1.083) -- ( 1.600,1.027) -- ( 1.650,0.974) -- ( 1.700,0.925) -- ( 1.750,0.878) -- ( 1.800,0.834) -- ( 1.850,0.792) -- ( 1.900,0.753) -- ( 1.950,0.715) -- ( 2.000,0.680) -- ( 2.050,0.647) -- ( 2.100,0.616) -- ( 2.150,0.587) -- ( 2.200,0.559) -- ( 2.250,0.533) -- ( 2.300,0.508) -- ( 2.350,0.485) -- ( 2.400,0.463) -- ( 2.450,0.442) -- ( 2.500,0.422) -- ( 2.550,0.403) -- ( 2.600,0.386) -- ( 2.650,0.369) -- ( 2.700,0.353) -- ( 2.750,0.338) -- ( 2.800,0.324) -- ( 2.850,0.311) -- ( 2.900,0.298) -- ( 2.950,0.286) -- ( 3.000,0.274) -- ( 3.050,0.263) -- ( 3.100,0.253) -- ( 3.150,0.243) -- ( 3.200,0.234) -- ( 3.250,0.225) -- ( 3.300,0.216) -- ( 3.350,0.208) -- ( 3.400,0.200) -- ( 3.450,0.193) -- ( 3.500,0.186) -- ( 3.550,0.179) -- ( 3.600,0.173) -- ( 3.650,0.167) -- ( 3.700,0.161) -- ( 3.750,0.155) -- ( 3.800,0.150) -- ( 3.850,0.145) -- ( 3.900,0.140) -- ( 3.950,0.135) -- ( 4.000,0.131) -- ( 4.050,0.127) -- ( 4.100,0.123);
\draw[line width=.6, red] (-4.100,0.084) -- (-4.050,0.088) -- (-4.000,0.092) -- (-3.950,0.096) -- (-3.900,0.100) -- (-3.850,0.104) -- (-3.800,0.109) -- (-3.750,0.114) -- (-3.700,0.119) -- (-3.650,0.124) -- (-3.600,0.130) -- (-3.550,0.136) -- (-3.500,0.142) -- (-3.450,0.149) -- (-3.400,0.156) -- (-3.350,0.164) -- (-3.300,0.171) -- (-3.250,0.180) -- (-3.200,0.189) -- (-3.150,0.198) -- (-3.100,0.208) -- (-3.050,0.219) -- (-3.000,0.230) -- (-2.950,0.242) -- (-2.900,0.254) -- (-2.850,0.267) -- (-2.800,0.282) -- (-2.750,0.297) -- (-2.700,0.312) -- (-2.650,0.329) -- (-2.600,0.347) -- (-2.550,0.366) -- (-2.500,0.387) -- (-2.450,0.408) -- (-2.400,0.431) -- (-2.350,0.455) -- (-2.300,0.481) -- (-2.250,0.509) -- (-2.200,0.538) -- (-2.150,0.569) -- (-2.100,0.602) -- (-2.050,0.638) -- (-2.000,0.675) -- (-1.950,0.715) -- (-1.900,0.757) -- (-1.850,0.802) -- (-1.800,0.850) -- (-1.750,0.900) -- (-1.700,0.954) -- (-1.650,1.010) -- (-1.600,1.070) -- (-1.550,1.133) -- (-1.500,1.200) -- (-1.450,1.271) -- (-1.400,1.345) -- (-1.350,1.422) -- (-1.300,1.504) -- (-1.250,1.589) -- (-1.200,1.678) -- (-1.150,1.770) -- (-1.100,1.866) -- (-1.050,1.965) -- (-1.000,2.067) -- (-0.950,2.172) -- (-0.900,2.279) -- (-0.850,2.387) -- (-0.800,2.497) -- (-0.750,2.606) -- (-0.700,2.716) -- (-0.650,2.824) -- (-0.600,2.930) -- (-0.550,3.033) -- (-0.500,3.132) -- (-0.450,3.225) -- (-0.400,3.313) -- (-0.350,3.393) -- (-0.300,3.465) -- (-0.250,3.527) -- (-0.200,3.579) -- (-0.150,3.621) -- (-0.100,3.651) -- (-0.050,3.669) -- ( 0.000,3.676) -- ( 0.050,3.669) -- ( 0.100,3.651) -- ( 0.150,3.621) -- ( 0.200,3.579) -- ( 0.250,3.527) -- ( 0.300,3.465) -- ( 0.350,3.393) -- ( 0.400,3.313) -- ( 0.450,3.225) -- ( 0.500,3.132) -- ( 0.550,3.033) -- ( 0.600,2.930) -- ( 0.650,2.824) -- ( 0.700,2.716) -- ( 0.750,2.606) -- ( 0.800,2.497) -- ( 0.850,2.387) -- ( 0.900,2.279) -- ( 0.950,2.172) -- ( 1.000,2.067) -- ( 1.050,1.965) -- ( 1.100,1.866) -- ( 1.150,1.770) -- ( 1.200,1.678) -- ( 1.250,1.589) -- ( 1.300,1.504) -- ( 1.350,1.422) -- ( 1.400,1.345) -- ( 1.450,1.271) -- ( 1.500,1.200) -- ( 1.550,1.133) -- ( 1.600,1.070) -- ( 1.650,1.010) -- ( 1.700,0.954) -- ( 1.750,0.900) -- ( 1.800,0.850) -- ( 1.850,0.802) -- ( 1.900,0.757) -- ( 1.950,0.715) -- ( 2.000,0.675) -- ( 2.050,0.638) -- ( 2.100,0.602) -- ( 2.150,0.569) -- ( 2.200,0.538) -- ( 2.250,0.509) -- ( 2.300,0.481) -- ( 2.350,0.455) -- ( 2.400,0.431) -- ( 2.450,0.408) -- ( 2.500,0.387) -- ( 2.550,0.366) -- ( 2.600,0.347) -- ( 2.650,0.329) -- ( 2.700,0.312) -- ( 2.750,0.297) -- ( 2.800,0.282) -- ( 2.850,0.267) -- ( 2.900,0.254) -- ( 2.950,0.242) -- ( 3.000,0.230) -- ( 3.050,0.219) -- ( 3.100,0.208) -- ( 3.150,0.198) -- ( 3.200,0.189) -- ( 3.250,0.180) -- ( 3.300,0.171) -- ( 3.350,0.164) -- ( 3.400,0.156) -- ( 3.450,0.149) -- ( 3.500,0.142) -- ( 3.550,0.136) -- ( 3.600,0.130) -- ( 3.650,0.124) -- ( 3.700,0.119) -- ( 3.750,0.114) -- ( 3.800,0.109) -- ( 3.850,0.104) -- ( 3.900,0.100) -- ( 3.950,0.096) -- ( 4.000,0.092) -- ( 4.050,0.088) -- ( 4.100,0.084);
\draw[line width=.6, green] (-4.100,0.061) -- (-4.050,0.064) -- (-4.000,0.067) -- (-3.950,0.071) -- (-3.900,0.074) -- (-3.850,0.078) -- (-3.800,0.082) -- (-3.750,0.087) -- (-3.700,0.091) -- (-3.650,0.096) -- (-3.600,0.101) -- (-3.550,0.107) -- (-3.500,0.113) -- (-3.450,0.119) -- (-3.400,0.126) -- (-3.350,0.133) -- (-3.300,0.140) -- (-3.250,0.148) -- (-3.200,0.157) -- (-3.150,0.166) -- (-3.100,0.176) -- (-3.050,0.186) -- (-3.000,0.197) -- (-2.950,0.209) -- (-2.900,0.221) -- (-2.850,0.235) -- (-2.800,0.249) -- (-2.750,0.264) -- (-2.700,0.280) -- (-2.650,0.297) -- (-2.600,0.316) -- (-2.550,0.336) -- (-2.500,0.357) -- (-2.450,0.379) -- (-2.400,0.403) -- (-2.350,0.429) -- (-2.300,0.456) -- (-2.250,0.485) -- (-2.200,0.516) -- (-2.150,0.550) -- (-2.100,0.585) -- (-2.050,0.623) -- (-2.000,0.663) -- (-1.950,0.706) -- (-1.900,0.751) -- (-1.850,0.799) -- (-1.800,0.851) -- (-1.750,0.905) -- (-1.700,0.963) -- (-1.650,1.024) -- (-1.600,1.089) -- (-1.550,1.157) -- (-1.500,1.229) -- (-1.450,1.304) -- (-1.400,1.384) -- (-1.350,1.467) -- (-1.300,1.554) -- (-1.250,1.644) -- (-1.200,1.739) -- (-1.150,1.836) -- (-1.100,1.937) -- (-1.050,2.040) -- (-1.000,2.147) -- (-0.950,2.255) -- (-0.900,2.365) -- (-0.850,2.476) -- (-0.800,2.588) -- (-0.750,2.699) -- (-0.700,2.809) -- (-0.650,2.918) -- (-0.600,3.023) -- (-0.550,3.125) -- (-0.500,3.223) -- (-0.450,3.314) -- (-0.400,3.400) -- (-0.350,3.478) -- (-0.300,3.547) -- (-0.250,3.607) -- (-0.200,3.658) -- (-0.150,3.698) -- (-0.100,3.727) -- (-0.050,3.744) -- ( 0.000,3.750) -- ( 0.050,3.744) -- ( 0.100,3.727) -- ( 0.150,3.698) -- ( 0.200,3.658) -- ( 0.250,3.607) -- ( 0.300,3.547) -- ( 0.350,3.478) -- ( 0.400,3.400) -- ( 0.450,3.314) -- ( 0.500,3.223) -- ( 0.550,3.125) -- ( 0.600,3.023) -- ( 0.650,2.918) -- ( 0.700,2.809) -- ( 0.750,2.699) -- ( 0.800,2.588) -- ( 0.850,2.476) -- ( 0.900,2.365) -- ( 0.950,2.255) -- ( 1.000,2.147) -- ( 1.050,2.040) -- ( 1.100,1.937) -- ( 1.150,1.836) -- ( 1.200,1.739) -- ( 1.250,1.644) -- ( 1.300,1.554) -- ( 1.350,1.467) -- ( 1.400,1.384) -- ( 1.450,1.304) -- ( 1.500,1.229) -- ( 1.550,1.157) -- ( 1.600,1.089) -- ( 1.650,1.024) -- ( 1.700,0.963) -- ( 1.750,0.905) -- ( 1.800,0.851) -- ( 1.850,0.799) -- ( 1.900,0.751) -- ( 1.950,0.706) -- ( 2.000,0.663) -- ( 2.050,0.623) -- ( 2.100,0.585) -- ( 2.150,0.550) -- ( 2.200,0.516) -- ( 2.250,0.485) -- ( 2.300,0.456) -- ( 2.350,0.429) -- ( 2.400,0.403) -- ( 2.450,0.379) -- ( 2.500,0.357) -- ( 2.550,0.336) -- ( 2.600,0.316) -- ( 2.650,0.297) -- ( 2.700,0.280) -- ( 2.750,0.264) -- ( 2.800,0.249) -- ( 2.850,0.235) -- ( 2.900,0.221) -- ( 2.950,0.209) -- ( 3.000,0.197) -- ( 3.050,0.186) -- ( 3.100,0.176) -- ( 3.150,0.166) -- ( 3.200,0.157) -- ( 3.250,0.148) -- ( 3.300,0.140) -- ( 3.350,0.133) -- ( 3.400,0.126) -- ( 3.450,0.119) -- ( 3.500,0.113) -- ( 3.550,0.107) -- ( 3.600,0.101) -- ( 3.650,0.096) -- ( 3.700,0.091) -- ( 3.750,0.087) -- ( 3.800,0.082) -- ( 3.850,0.078) -- ( 3.900,0.074) -- ( 3.950,0.071) -- ( 4.000,0.067) -- ( 4.050,0.064) -- ( 4.100,0.061);
\draw[line width=.6, blue] (-4.100,0.046) -- (-4.050,0.048) -- (-4.000,0.051) -- (-3.950,0.054) -- (-3.900,0.057) -- (-3.850,0.061) -- (-3.800,0.065) -- (-3.750,0.069) -- (-3.700,0.073) -- (-3.650,0.077) -- (-3.600,0.082) -- (-3.550,0.087) -- (-3.500,0.092) -- (-3.450,0.098) -- (-3.400,0.104) -- (-3.350,0.111) -- (-3.300,0.118) -- (-3.250,0.126) -- (-3.200,0.134) -- (-3.150,0.143) -- (-3.100,0.152) -- (-3.050,0.162) -- (-3.000,0.173) -- (-2.950,0.184) -- (-2.900,0.197) -- (-2.850,0.210) -- (-2.800,0.224) -- (-2.750,0.239) -- (-2.700,0.256) -- (-2.650,0.273) -- (-2.600,0.292) -- (-2.550,0.312) -- (-2.500,0.333) -- (-2.450,0.356) -- (-2.400,0.381) -- (-2.350,0.407) -- (-2.300,0.436) -- (-2.250,0.466) -- (-2.200,0.498) -- (-2.150,0.533) -- (-2.100,0.569) -- (-2.050,0.609) -- (-2.000,0.651) -- (-1.950,0.696) -- (-1.900,0.743) -- (-1.850,0.794) -- (-1.800,0.848) -- (-1.750,0.905) -- (-1.700,0.966) -- (-1.650,1.030) -- (-1.600,1.098) -- (-1.550,1.170) -- (-1.500,1.245) -- (-1.450,1.324) -- (-1.400,1.407) -- (-1.350,1.494) -- (-1.300,1.585) -- (-1.250,1.679) -- (-1.200,1.777) -- (-1.150,1.877) -- (-1.100,1.981) -- (-1.050,2.088) -- (-1.000,2.197) -- (-0.950,2.307) -- (-0.900,2.419) -- (-0.850,2.532) -- (-0.800,2.645) -- (-0.750,2.757) -- (-0.700,2.868) -- (-0.650,2.976) -- (-0.600,3.081) -- (-0.550,3.183) -- (-0.500,3.279) -- (-0.450,3.370) -- (-0.400,3.454) -- (-0.350,3.530) -- (-0.300,3.598) -- (-0.250,3.657) -- (-0.200,3.706) -- (-0.150,3.745) -- (-0.100,3.773) -- (-0.050,3.790) -- ( 0.000,3.796) -- ( 0.050,3.790) -- ( 0.100,3.773) -- ( 0.150,3.745) -- ( 0.200,3.706) -- ( 0.250,3.657) -- ( 0.300,3.598) -- ( 0.350,3.530) -- ( 0.400,3.454) -- ( 0.450,3.370) -- ( 0.500,3.279) -- ( 0.550,3.183) -- ( 0.600,3.081) -- ( 0.650,2.976) -- ( 0.700,2.868) -- ( 0.750,2.757) -- ( 0.800,2.645) -- ( 0.850,2.532) -- ( 0.900,2.419) -- ( 0.950,2.307) -- ( 1.000,2.197) -- ( 1.050,2.088) -- ( 1.100,1.981) -- ( 1.150,1.877) -- ( 1.200,1.777) -- ( 1.250,1.679) -- ( 1.300,1.585) -- ( 1.350,1.494) -- ( 1.400,1.407) -- ( 1.450,1.324) -- ( 1.500,1.245) -- ( 1.550,1.170) -- ( 1.600,1.098) -- ( 1.650,1.030) -- ( 1.700,0.966) -- ( 1.750,0.905) -- ( 1.800,0.848) -- ( 1.850,0.794) -- ( 1.900,0.743) -- ( 1.950,0.696) -- ( 2.000,0.651) -- ( 2.050,0.609) -- ( 2.100,0.569) -- ( 2.150,0.533) -- ( 2.200,0.498) -- ( 2.250,0.466) -- ( 2.300,0.436) -- ( 2.350,0.407) -- ( 2.400,0.381) -- ( 2.450,0.356) -- ( 2.500,0.333) -- ( 2.550,0.312) -- ( 2.600,0.292) -- ( 2.650,0.273) -- ( 2.700,0.256) -- ( 2.750,0.239) -- ( 2.800,0.224) -- ( 2.850,0.210) -- ( 2.900,0.197) -- ( 2.950,0.184) -- ( 3.000,0.173) -- ( 3.050,0.162) -- ( 3.100,0.152) -- ( 3.150,0.143) -- ( 3.200,0.134) -- ( 3.250,0.126) -- ( 3.300,0.118) -- ( 3.350,0.111) -- ( 3.400,0.104) -- ( 3.450,0.098) -- ( 3.500,0.092) -- ( 3.550,0.087) -- ( 3.600,0.082) -- ( 3.650,0.077) -- ( 3.700,0.073) -- ( 3.750,0.069) -- ( 3.800,0.065) -- ( 3.850,0.061) -- ( 3.900,0.057) -- ( 3.950,0.054) -- ( 4.000,0.051) -- ( 4.050,0.048) -- ( 4.100,0.046);
\end{tikzpicture}}
\end{document}

References

Keywords

«Student.cin», «Factorial», «Student Distribution», «[[]]»,