Based on what I have seen, however, I wish I had another plot, this time the Poisson distribution as you have presented it, only for lambda = 18 (3 hour expected network block production), and running out to k = 36.
While I am wishing, I also want a numeric table of the cumulative distribution function for the same distribution.
While I am wishing, I also want a numeric table of the cumulative distribution function for the same distribution.
here you are:
1. probability of exactly n block within 3 hours:
2. cummulative numeric, that is probability to have <= n blocks within 3 hours:
Code:
{
{0, 1.523E-8},
{1, 2.8937E-7},
{2, 2.75663E-6},
{3, 0.0000175602},
{4, 0.0000841761},
{5, 0.000323993},
{6, 0.00104345},
{7, 0.00289347},
{8, 0.00705601},
{9, 0.0153811},
{10, 0.0303663},
{11, 0.0548874},
{12, 0.0916692},
{13, 0.142598},
{14, 0.208077},
{15, 0.286653},
{16, 0.37505},
{17, 0.468648},
{18, 0.562245},
{19, 0.650916},
{20, 0.73072},
{21, 0.799124},
{22, 0.85509},
{23, 0.89889},
{24, 0.93174},
{25, 0.955392},
{26, 0.971766},
{27, 0.982682},
{28, 0.9897},
{29, 0.994056},
{30, 0.996669},
{31, 0.998187},
{32, 0.99904},
{33, 0.999506},
{34, 0.999752},
{35, 0.999879},
{36, 0.999942},
{37, 0.999973},
{38, 0.999988}
}
{0, 1.523E-8},
{1, 2.8937E-7},
{2, 2.75663E-6},
{3, 0.0000175602},
{4, 0.0000841761},
{5, 0.000323993},
{6, 0.00104345},
{7, 0.00289347},
{8, 0.00705601},
{9, 0.0153811},
{10, 0.0303663},
{11, 0.0548874},
{12, 0.0916692},
{13, 0.142598},
{14, 0.208077},
{15, 0.286653},
{16, 0.37505},
{17, 0.468648},
{18, 0.562245},
{19, 0.650916},
{20, 0.73072},
{21, 0.799124},
{22, 0.85509},
{23, 0.89889},
{24, 0.93174},
{25, 0.955392},
{26, 0.971766},
{27, 0.982682},
{28, 0.9897},
{29, 0.994056},
{30, 0.996669},
{31, 0.998187},
{32, 0.99904},
{33, 0.999506},
{34, 0.999752},
{35, 0.999879},
{36, 0.999942},
{37, 0.999973},
{38, 0.999988}
}