Poisson process

-12/02 3. [5 points] Suppose that the number of customers arriving at the Woori Bank follows a Poisson process with a rate of Aw = 0.5 per minute, the number of customers arriving at the Hana Bank follows a Poisson process with a rate of An = 0.2 per minute, and the two Poisson processes are independent. Let( We )be the waiting time to have the kth customer at the Woori Bank and /, be the waiting time to have the kth customer at the Hana Bank. Find the probability distribution of the random variable Wa H 2 and explain why.Consider a birth-and-death process with just three attainable states (0, 1, and 2), for which the steady-state probabilities are PO, P1, and P2, respectively. The birth-and-death rates are summarized in the following table: state Birth Death rate rate 0 1 1 1 2 2 2 a)Construct the rate diagram for this birth-and-death process. b) Develop the balance equation. c) Solve these equations to find PO, P1, and P2 d) Use the general formulas for the birth-and-death process to calculate PO, P1 and P2.Also calculate L, Lq, W, and Wq.Recall the Poisson process that we covered during the lecture. We showed that if earthquakes happen following a Poisson process, the time interval between two consecutive earthquakes is exponentially distributed. This also implies that if an earthquake just happened, the time of the next one (1) earthquake follows exponential distribution. Now, we want to generalize this result. Suppose that earthquakes near San Francisco happens following a Poisson process 2 and an earthquake just happened. Find the probability that in the next 5 years, there are less than ten (10) earthquakes. For this question, Could you tell me how to distinguish Binomial distribrition, Exponential distribution, Beta distribution, uniform distribution Suppose you are an telephone operator of a company and your job is to answer the phones. Let the waiting time between two phone calls be T. Decide a distribution of T. O Binomial Distribution O Exponential Distribution O Beta Distribution O Uniform Distribution