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Let Y denote the number of positive COVID-19 tests each day in a test centre. Suppose that 0.25% positive tests were observed among 4000 people. (a) Explain why Y follows a Poisson distribution with A = 10. (b) what are the mean, / = E(Y), and standard deviation of o = VVar(Y)? (c) A warning flag is raised if, on any day, Y exceeds p + 20, Calculate the probability that a warning flag is raised, P(Y > # + 20). (d) The daily cost of quarantining positive cases is a random variable Q given by Q = 10Y2 + 100(Y - 10)2 + 10000 Calculate E(Q)