定繊生糸における異種繭糸数の確率分布〔原科繭の合併に関する研究-4-〕

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On the fixed size raw silk thread reeled from the compounded cocoon population, we consider the probability distribution of the number of remarkable cocoon filaments in the thread. Let a random variable Vi be the number of remarkable filaments and the average number of reeling cocoon filaments E[K] be shown as, E[K]=K1+d, where K1 is th integer value, and d is a decimal fraction. Then the probability Pr{Vi=ri} is approximately given by the equationPr{Vi=ri}=(K1ri)piri(1-pi)K1-riω1+(K1+1ri)piri(1-pi)K1+1-riω2, where pi is the cocoon filament ratio of remarkable cocoon lot and ω1=1-d, ω1+ω2=1. From the equation, it is known that the expectation of Vi, E[Vi] and the variance V[Vi] are given by the relationsE[Vi]=piE[K]V[Vi]=pi(1-pi)E[K].
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