<jupyter_start><jupyter_text>$$ p_0 = \frac{\tau T}{4 \tau_0^2}$$  $$ \sigma_{p_0}^2 = \left(\frac{\partial p_0}{\partial \tau}\right)^2 \sigma_\tau^2 + \left(\frac{\partial p_0}{\partial \tau}\frac{\partial p_0}{\partial T}\right) \mathrm{cov}(\tau,T)+\left(\frac{\partial p_0}{\partial T}\right)^2 \sigma_T^2 +\left(\frac{\partial p_0}{\partial \tau_0}\right)^2 \sigma_{\tau_0}^2 $$$$ \sigma_{p_0}^2 = \left(\frac{T  \sigma_\tau}{4  \tau_0^2} \right)^2 +                \left(\frac{\tau  T }{16 \tau_0^4} b  \theta^2 T^2\right) +                \left(\frac{\tau  \sigma_T}{4 \tau_0^2} \right)^2 +                \left(\frac{\tau  T }{2 \tau_0^3}  \sigma_{\tau_0}\right)^2 $$<jupyter_code>sigma_p0_sq = ((T * sigma_tau / 4 / tau0**2)**2 + 
               (tau * T / 16 / tau0**4) * b * theta**2 * T**2 + 
               (tau * sigma_T / 4 / tau0**2)**2 + 
               (tau * T / 2 / tau0**3 * sigma_tau_0)**2)
sqrt(sigma_p0_sq).simplify()
print(sqrt(sigma_p0_sq).simplify())<jupyter_output>sqrt(p0)*sqrt(-(-Gamma*b*delta**2*p0**2*tau0**2*(-b**2 + 1)**(3/2) - 4*Gamma*delta**2*p0*sigma_tau_0**2*(-b**2 + 1)**(5/2) + p0**2*sigma**2*tau0*(b**2 - 1) - 3*sigma**2*tau0*(-b**2 + 1)**3)/(-b**2 + 1)**(5/2))/(sqrt(Gamma)*delta*tau0)
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