<jupyter_start><jupyter_text>p_hit_event = .1 is the desired probability of a hit occuring in a typical on-detector bin for a random event.num_hits_event ~= 100000 is average number of hits in an eventnum_on_dectector_bins = 1M = num_hits_event/p_event_hit is the number of on-detector bins needed to produce average hit probability p_hit.num_cylinder_bins = number of bins on the surface of cylindrical detectorsnum_disk_bins = number of bins on the surface of disk detectorsR_binstheta_binsz_binsR_bins is constructed using disk_hitsz_bins is constructed using cylinder_hitstheta_bins is constructed using all hitsnum_disk_bins ~= len(R_bins)\*len(theta_bins)num_cylinder_bins ~= len(z_bins)\*len(theta_bins)num_on_detector_bins ~= num_disk_bins\*num_cylinder_binsInitial guess will be len(R_bins) = len(theta_bins) = len(z_bins) = sqrt(num_on_detector_bins/2)***p_hit = p_hit_event/num_hits_event = ~1/num_on_detector_bins ~= 1E-6 is probability that a randomly chosen hit will occur in a typical bin. Second approximate equality holds when p_hit_event is smallp_hit_cylinder ~= z_q\*theta_qp_hit_disk ~= R_q\*theta_qp_hit ~= mean(R_q\*theta_q, z_q\*theta_q)Initially choose R_q = theta_q = sqrt(p_hit) = 1E-3<jupyter_code>disk_hits.z.value_counts()<jupyter_output><empty_output>
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