x = linspace(-10.,10.,1000.)
a=1.3
b=2.
p = (1./b/sqrt(2*np.pi))*exp(-(x-a)**2/2./b**2)
plot(x,p)
plot(array([1,1])*a,[0,0.3],'r--')
text(a,0.2,' a',fontsize='large')
plot(array([1,1])*a+sqrt(2)*b,[0,0.3],'r--')
text(a+sqrt(2)*b,0.2,' $a+\sqrt{2}b$',fontsize='large')
plot(array([1,1])*a-sqrt(2)*b,[0,0.3],'r--')
text(a-sqrt(2)*b,0.2,' $a-\sqrt{2}b$',fontsize='large',horizontalalignment='right')
plot([-10,10],(1./b/sqrt(2*np.pi))*exp(-1)*array([1,1]),'r--')
text(a-sqrt(2)*b,(1./b/sqrt(2*np.pi))*exp(-1),r' $\frac{1}{b\sqrt{2\pi}}e^{-1}$',fontsize='large',horizontalalignment='right')
xlabel('$x\ \ [V]$')
ylabel('$p(x)\ \ [V^{-1}]$')
title('Normal Distribution a=%1.2f, b=%1.2f'%(a,b))
savefig('images/NormalDist.png')