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Passengers barrive at a Metro station following a Poisson distribution with parameter 50. The train arrival time is distributed on the interval (0, 1) with density function 2t. Determine: E(# of people who will board the train given that the train arrives at time .5) Var(# of people who will board the train given that the train arrives at time .5) E(train arrival time) Var(train arrival time) E(# of people who will board the train) Var(# of people who will board the train)