157 Supplementary files Probability distributions of sum over persons Denote the value of any of the variables SDML, EMOL, TECHL, SDMH, EMOH, TECHH C M Y CM MY CY CMY K equation-75.pdf 1 07-03-2024 22:25 , TECHL−SDML, TECHH−SDMH, EMOL−SDML, C M Y CM MY CY CMY K equation-76.pdf 1 07-03-2024 22:25 or EMOH−SDMH C M Y CM MY CY CMY K EMO_H-SDM_H.pdf 1 07-03-2024 22:26 , summed over n C M Y CM MY CY CMY K n.pdf 1 persons, as S(n) C M Y CM MY CY CMY K S(n).pdf 1 07-03-2024 22:28 . The probability distribution of S(1) C M Y CM MY CY CMY K S(1).pdf 1 07-03-2024 22:22 is just the distribution within a single person which is given in table A1 or A4 or A6. Once the distribution of S(n) C M Y CM MY CY CMY K S(n).pdf 1 07-03-2024 22:28 is known for some n ∈ℕ C M Y CM MY CY CMY K n€N.pdf 1 07-03-2024 22:23 , the distribution of S(n +1) C M Y CM MY CY CMY K S(n+1).pdf 1 07-03-2024 22:28 can be computed by P(S(n +1) =k) = 3 ∑ i=−3 P(S(n) =k −i)P(S(1) =i) C M Y CM MY CY CMY K equation-84.pdf 1 07-03-2024 22:24 Thus, from S(1) C M Y CM MY CY CMY K S(1).pdf 1 07-03-2024 22:22 we can compute S(2) C M Y CM MY CY CMY K S(2).pdf 1 07-03-2024 22:22 , and from S(2) C M Y CM MY CY CMY K S(2).pdf 1 07-03-2024 22:22 we can compute S(3) C M Y CM MY CY CMY K S(3).pdf 1 07-03-2024 22:28 , and from S(3) C M Y CM MY CY CMY K S(3).pdf 1 07-03 we can compute S(4) C M Y CM MY CY CMY K S(4).pdf 1 07-03-2024 22:28 , etc. In this way we can compute the probability distribution of S(15) C M Y CM MY CY CMY K S(15).pdf 1 07-03-202 and S(23) C M Y CM MY CY CMY K S(23).pdf 1 , which were used for the tests of complexity and job satisfaction, respectively. For example, if we take S(1) =SDML C M Y CM MY CY CMY K S(1)=SDM-L.pdf 1 07-03-2024 22:22 , then the probability distribution is given in table A1. For two persons who respond independently of each other, the probabilities that the first person has SDML(1) =k1 C M Y CM MY CY CMY K SDM_L(1)=k1).pdf 1 07-03-2024 22:27 and the second person has SDML(2) =k2 C M Y CM MY CY CMY K SDM_L(2)=k2.pdf 1 07-03-2024 22:27 is given in table A7. Table A7: Joint probabilities of SDML C M Y CM MY CY CMY K SDM-L.pdf 1 07-03-2024 22:27 in two independent persons. k2 C M Y CM MY CY CMY K k2.pdf 1 07-03-2024 22:24 0 1 2 3 total k1 C M Y CM MY CY CMY K k1.pdf 1 07-03-2024 22:24 0 0.0851 0.1531 0.0510 0.0024 0.2917 1 0.1531 0.2756 0.0919 0.0044 0.5250 2 0.0510 0.0919 0.0306 0.0015 0.1750 3 0.0024 0.0044 0.0015 0.0001 0.0083 total 0.2917 0.5250 0.1750 0.0083 Cells with the same color in table A7 have the same value of k1 +k2 C M Y CM MY CY CMY K k1+k2.pdf 1 07-03-2024 22:24 , and their probabilities should be added. From this we obtain the distribution of S(2) C M Y CM MY CY CMY K S(2).pdf 1 07-03-2024 22:22 , given in table A8. Next, the process is repeated with S(1) C M Y CM MY CY CMY K S(1).pdf 1 07-03-2024 22:22 and S(2) C M Y CM MY CY CMY K S(2).pdf 1 07-03-2024 22:22 to obtain S(3) C M Y CM MY CY CMY K S(3).pdf 1 07-03-2024 22:28 , and this continues until we have S(23) C M Y CM MY CY CMY K S(23).pdf 1 (because the data came from twenty-three persons). Table A8: Probability distribution of S(2) C M Y CM MY CY CMY K S(2).pdf 1 07-03-2024 22:22 if S(1) =SDML C M Y CM MY CY CMY K S(1)=SDM-L.pdf 1 07-03-2024 22:22 . k C M Y CM MY CY CMY K k.pdf 1 07-03-2024 22:24 Computation P(S(2) =k) C M Y CM MY CY CMY K P(S(2)=k).pdf 1 07-03-202 0 0.0851 0.0851 1 0.1531 + 0.1531 0.3063 2 0.0510 + 0.2756 + 0.0510 0.3777 3 0.0024 + 0.0919 + 0.0919 + 0.0024 0.1886 4 0.0044 + 0.0306 + 0.0044 0.0394 5 0.0015 + 0.0015 0.0029 6 0.0001 0.0001 A
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