def NPV_prob(rho,g,eff,H,delta_t,p,Q,mean,std,a,b):
t = np.arange(0,100000,0.5)
PV = simps(np.exp(-t*r)*rho*g*eff*H*delta_t*p/1000*EV_flow(mean,std,Q), t)
NPVal = PV - cost(a, b, Q)
return NPVal
# declare matrices to store data
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