N C 1 7 C 1 : 1 1 : 1 1 N 1 C 3 : (2+2+2) 3 6 C (2 3)!/(2!) ,833,153,121, N M ( ) #holidays partitions

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1 v (11 3 ) (4 29 ) (12 23 ) N = 365 M = 125 P (M, N n) n 2 7 (1) 7 1 (1+6) (2+5) ( ) ( ) 4 1 1

2 N C 1 7 C 1 : 1 1 : 1 1 N 1 C 3 : (2+2+2) 3 6 C (2 3)!/(2!) ,833,153,121, N M ( ) #holidays partitions (7) (1+6) (1+1+5) ( ) ( ) ( ) ( ) (2+5) (1+2+4) ( ) ( ) (3+4) (1+3+3) ( ) (2+2+3) Partition Number ( ) = 15 #cases E E E E E+17 1 / Probability 1 #holidays 6 1: M = M = M =

3 partition number N 2: N (partition number) 3 (Monte Carlo:MC) M (M = 125) 106 (Root Mean Square: RMS) [1] RMS 30 ( 31 ) ± ±

4 Number of holidays M=50 Mean: M=125 RMS : M=200 Mean: M=300 RMS : M=500 Mean: RMS : Mean: RMS : Mean: RMS : : (M = 50) (M = 125) (M = 200) (M = 300) (M = 500) 1: ( 12 ) [1] % (RMS) ± 0.20 (RMS) 4

5 Number of holidays M=50 Mean: M=125 RMS : M=200 Mean: M=300 RMS : M=500 Mean: RMS : Mean: RMS : Mean: RMS : : (M = 50) (M = 125) (M = 200) (M = 300) (M = 500) Q(M n) n M M n n M M 1 2 Q(M n) = n M n C 1 Q(M 1) n C 2 Q(M 2) (1) n 1 M min(m,n 1) Q(M n) = n M nc i Q(M i) (2) Q(M n) N n M i=1 P (M, N n) = N C n Q(M n) N M (3) (2) Q(M i) i = 1 M P (M, N n) 5

6 4.2 Q(M i) N M = Python P (M, N n) ( ) Python O( ) ( ) 5 P (125, 365 n) RMS #emperos=125 average= days in 365 days sigma= 3.48 days 0.08 PDF #holidays 5: 5 1 P holiday N P holiday 1 P holiday 5.1 M N ( ) ( ) 1. α 1/N 1 α. 6

7 2: Table of birthdays. : a brithday, : not a birthday. Day 0 1 N-1 Person 0 1 M ( 1 ) 1 P holiday P workday 1 P holiday 5.2 M N [α + (1 α)] M+N = 1 (4) ( ) 0 2 P workday P holiday = P workday N C 1 α 1 (1 α) N 1 (5) M [ NC 1 α 1 (1 α) N 1] M (6) (1 α) N 1 C 1 α 1 (1 α) N 2 (7) M [ (1 α) N 1 C 1 α 1 (1 α) N 2] M (8) 7

8 5.5 [ (1 α) N 1 C 1 α 1 (1 α) N 2] M P workday = [ N C 1 α 1 (1 α) N 1 ] M (9) [ (1 α) (N 1)α 1 (1 α) N 2 ] M = Nα 1 (1 α) N 1 (10) = [1 1/N] M (11) =(1 α) M (12) P holiday =1 P workday = 1 (1 α) M = 1 (1 1/N) M (13) P workday = (1 α) M 0 2 M 5.6 M = 125, N = 365 P holiday =1 (1 1/365) 125 = 0.29 (14) µ µ =N P holiday = 106( ). (15) 5.7 P holiday N 2 RMS RMS = N P holiday (1 P holiday ) = 8.7( ). (16) MC 2 P holiday ( 1 ) N N M 1 P workday =(1 1/N) M (17) 8

9 *(1-(1-1./365.)**x) 10 sqrt(365.*(1-(1-1./365.)**x)*(1-1./365.)**x) Mean number of holidays RMS of holidays Number of persons Number of persons 6: 2 7: 2 RMS 3: Table of birthdays. : a brithday. Day 0 1 N-1 Person 0 1 M Python (64bit ) 1 M n NC n Q(M n)/n M = N [ 1 (1 1/N) M] (18) n M 1000 RMS 9 ( ) 9

10 (a) formula MC (b) 8: (a): ( ) ( ) M ( ) (b): (RMS/ 10 5 ) formula MC + simple 9: RMS M ( ) ( ) ( ) ( ) 10

11 7 125 [2] [3, 4] AKB (3) RMS 3.7 NMB48 SKE48 HKT48 [4] [5] [6] ,102 12, ± : ± 3.5 n = N [ 1 ( 1 1 ) ] M N (19) (20) 11

12 jurist 5 moviedir n - nexpected 0 5 hello_pro NMB48 HKT48 AKB48 Nogizaka46 SKE48 kyoutei figurescating sumo medicineboxing baseball basketball politicians prowrestling golf volleyball Takarazuka actors 10 translators tennis 15 jockey M 11: n = n n NC n Q(M n)/n M (21) (RMS) M MPPC [1] [accessed 2017 Dec. 26]. syussyo-4/syussyo1-2.html. [2] Wikipedia [accessed 2017 Dec. 26]. [3] AKB [accessed 2017 Dec. 26]. 12

13 [4] [accessed 2017 Dec. 26]. [5] [accessed 2017 Dec. 26]. index/s_birthday/. [6] ( ) [accessed 2017 Dec. 26]. 13

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