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In: Statistics and Probability

Amid COVID-19, there are fewer cars running in the street. Suppose after 10am the cars pass...

Amid COVID-19, there are fewer cars running in the street. Suppose after 10am the cars pass through the traffic light in front of the gate of QC according to a Poisson process with rate 2 per minute. Let Y denote the waiting time for the arrival of the fourth car. (a) (8pts) Find the probability that the fourth arrival is between 10:01am and 10:03am. That is P(1 < Y < 3). (b) (6pts) Let W be a random variable independent of Y . Suppose W has gamma distribution with parameters α = 3, θ = 1 2 . Find the correlation between Y and W − Y .

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