8.13 Show that if Xi,i = 1, 2,... , n, are n independent Poisson random variables each with parameter λi, then the random variable Y deﬁned as: n Y = , Xi i=1 i=1 is also a Poisson random variable, with parameter λ∗ = ),n λi. 8.14 The number of yarn breaks per shift in a commercial ﬁber spinning machine is a Poisson variable with λ = 3. Determine the probability of not experiencing any yarn break in a particular shift. What is the probability of experiencing more than 3 breaks per shift?
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