human
Solve the following python programming problem given the following code:
# Here, defining population to match what was fit for in the paper
from exosyspop.populations import PlanetPopulation

import astropy.constants as const
RJUP = const.R_jup.cgs
RSUN = const.R_sun.cgs
REARTH = const.R_earth.cgs

class LongPeriodPlanetPopulation(PlanetPopulation):
    """
    Poisson Population in two bins: 0.1-0.4 RJup and 0.4-1.0 RJup
    
    From 2 to 25 years, with beta eccentricity distribution
    """
    min_period = 2*365.25
    max_period = 25*365.25
    
    vol1 = (np.log(0.4) - np.log(0.1))*(np.log(max_period) - np.log(min_period))
    vol2 = (np.log(1) - np.log(0.4))*(np.log(max_period) - np.log(min_period))
    
    param_names = ('Gam1', 'Gam2', 'beta_a', 'beta_b')
    default_params = {'Gam1':0.4, 'Gam2':0.18,
                      'beta_a':1.12, 'beta_b':3.09}
    
    def _sample_period(self, N):
        lo = np.log(self.min_period)
        hi = np.log(self.max_period)
        logp = np.random.random(N)*(hi - lo) + lo
        return np.exp(logp)
    
    def _sample_Np(self, N):
        Gam1, Gam2 = self._get_params(['Gam1', 'Gam2'])
        
        N_pl = Gam1*self.vol1 + Gam2*self.vol2 # Sum of both bins is total rate
        return np.random.poisson(N_pl, size=N)
    
    def _sample_Rp(self, N):
        Gam1, Gam2 = self._get_params(['Gam1', 'Gam2'])
        Nexp1 = Gam1*self.vol1
        Nexp2 = Gam2*self.vol2
        
        # Assign radii uniformly in each bin, with appropriate ratio given to each bin
        f1 = Nexp1 / (Nexp1 + Nexp2)
        u = np.random.random(N)
        in_1 = u < f1
        in_2 = u >= f1
        N1 = in_1.sum()
        N2 = in_2.sum()
        
        Rp = np.ones(N)
        lo1, hi1 = np.log(0.1), np.log(0.4)
        lo2, hi2 = np.log(0.4), np.log(1)
        Rp[in_1] = np.exp(np.random.random(N1)*(hi1 - lo1) + lo1)
        Rp[in_2] = np.exp(np.random.random(N2)*(hi2 - lo2) + lo2)
        return Rp * RJUP/RSUN

plpop = LongPeriodPlanetPopulation(targets)

plpop._train_trap(N=1000);
#_ = plpop.observe() # There was a point where this was...
Given the above code, generate some markdown instructions for it.
assistant
#Here was fit for in the paper
.

Simulate detected population of planets
As a good sanity check, let's make sure we reproduce the detected population of planet signals, given the population model constrained in the paper.