Cfrgtkky

Could you help me to draw the last option using in/out draw? Other way is ok.

documentclass{article}  



usepackage{tikz}



begin{document}

begin{tikzpicture}[scale=.71]



draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick](0,0) to[out=10, in=199] (1.25,2);



draw[red, thick](1.25,2) to[out=-5, in=170] (3.75,0.5);





end{tikzpicture}



  begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick](1.5,0) to[out=50, in=119] (2,2.5);



draw[red, thick](2,2.5) to[out=-70, in=111] (2.5,0);





end{tikzpicture}





 begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.414);

draw(4.15,0) node[right] {$E$};

draw(0,2.41) node[above] {$p(E)$};

draw[red, thick](0.2,2.2) to[out=-70, in=179] (3.6,.55);







end{tikzpicture}





 begin{tikzpicture}[scale=.71 ]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.414);

draw(4.15,0) node[right] {$E$};

draw(0,2.41) node[above] {$p(E)$};

draw[red, thick](0.3,.0) to[out=70, in=179] (1.2,1.7);

end{tikzpicture}



end{document}

I would like to argue that the simplest way is to define some standard functions and plot a linear combination of them.

documentclass{article}  



usepackage{tikz}



begin{document}

begin{tikzpicture}[scale=.71]



draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick](0,0) to[out=10, in=199] (1.25,2);



draw[red, thick](1.25,2) to[out=-5, in=170] (3.75,0.5);





end{tikzpicture}



  begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick](1.5,0) to[out=50, in=119] (2,2.5);



draw[red, thick](2,2.5) to[out=-70, in=111] (2.5,0);





end{tikzpicture}





 begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.414);

draw(4.15,0) node[right] {$E$};

draw(0,2.41) node[above] {$p(E)$};

draw[red, thick](0.2,2.2) to[out=-70, in=179] (3.6,.55);







end{tikzpicture}





 begin{tikzpicture}[scale=.71,declare function={

 fcont(x)=x*x*exp(-2*x);

 fpeak(x,y,z)=exp(-(x-y)*(x-y)/(z*z));}]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.414);

draw(4.15,0) node[right] {$E$};

draw(0,2.41) node[above] {$p(E)$};

draw[red, thick] plot[smooth,variable=x,domain=0:3.5,samples=81]

({x+0.5},{10*fcont(x)+1.3*fpeak(x,1.3,0.05)+0.9*fpeak(x,1,0.05)});

end{tikzpicture}



end{document}

I could not resist to draw the other curves using the same strategy, and also arranging the plots in a 2x2 scheme.

documentclass{article}  

usepackage{subcaption}

usepackage{tikz}

tikzset{declare function={

 fcont(x,b)=x*x*exp(-2*b*x);

 fpeak(x,y,z)=exp(-(x-y)*(x-y)/(z*z));}}

begin{document}



begin{figure}

centering

begin{subfigure}{0.4textwidth}

centering

begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick] plot[smooth,variable=x,domain=0:4,samples=81]

({x},{8*fcont(x,0.8)});

end{tikzpicture}

caption{I look like a Planck distribution.}label{fig:Planck}

end{subfigure}

quad

begin{subfigure}{0.4textwidth}

centering

begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick] plot[smooth,variable=x,domain=1.6:2.4,samples=81]

({x},{2.5*(fpeak(x,2,0.2)-fpeak(1.6,2,0.2))});

end{tikzpicture}

caption{I look like a Gaussian peak.}label{fig:Gauss}

end{subfigure}\

begin{subfigure}{0.4textwidth}

centering

begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick] plot[smooth,variable=x,domain=0:4,samples=81]

({x},{2*exp(-x)});

end{tikzpicture}

caption{I look like a an exponentially decaying function.}label{fig:Exp}

end{subfigure}

quad

begin{subfigure}{0.4textwidth}

centering

begin{tikzpicture}[scale=.71]

draw[->](0,0)--(4.05,0);

draw[->](0,-.3)--(0,2.14);

draw(4.15,0) node[right] {$E$};

draw(0,2.1) node[above] {$p(E)$};

draw[red, thick] plot[smooth,variable=x,domain=0:3.5,samples=81]

({x+0.5},{10*fcont(x,1)+1.3*fpeak(x,1.3,0.05)+0.9*fpeak(x,1,0.05)});

end{tikzpicture}

caption{I look like a Planck distribution plus two Gaussian

peaks.}label{fig:Spectrum}

end{subfigure}

caption{Cartoons of a few distributions that often occur in science.}

end{figure}

end{document}

I had to adjust the prefactors by trial and error. This is not necessary if you switch to pgfplots, where you can use group plots to arrange the plots in a 2x2 scheme, too.