A shop is open from 10am to 6pm. Customers arrive in the shop according to a...

  

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A shop is open from 10am to 6pm. Customers arrive in the shop according to a non- homogeneous Poisson process with an intensity function, which equals zero at opening, 4 customers per hour at noon, 6 customers per hour at 2pm, 2 customers per hour at 4pm and zero at closing; between any two consequent afore-mentioned times, it is linear (hence, for example, the rate is M(t) = 2(t – 10) for 10 < t < 12 - I suggest you consider military time for this!) a) Find the distribution of the number of customers on a given day. b) Find the probability that no customer arrives until noon. c) Find the cumulative distribution function of the time of the first arrival. A shop is open from 10am to 6pm. Customers arrive in the shop according to a non- homogeneous Poisson process with an intensity function, which equals zero at opening, 4 customers per hour at noon, 6 customers per hour at 2pm, 2 customers per hour at 4pm and zero at closing; between any two consequent afore-mentioned times, it is linear (hence, for example, the rate is M(t) = 2(t – 10) for 10 < t < 12 - I suggest you consider military time for this!) a) Find the distribution of the number of customers on a given day. b) Find the probability that no customer arrives until noon. c) Find the cumulative distribution function of the time of the first arrival.

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