6)For a rate A Poisson process we try tostop at the last event before some fixedtime T. Our strategy will be to stop atthe first event after some time s. Welose if there are no more events after sand before T or if the next event after sis not the last event before T. What isthe probability of winning for s fixed?What value of s maximizes thisprobability? What is the maximum value?

Answered: 6)For a rate A Poisson process we try…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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8.
Roll two fair dice. Use the Poisson approximation to find the probability that you will rollat least one double (meaning both dice land on the same value) in 24 trials. How does this compare tothe exact value? Answer as if explaining to someone.
Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.
i need help
Could you solve (i), (ii), (iii)? Thank you.
In game of roulette, a player can bet on the 1/38 probabilty of metal batt landa on 1the player gets to keep the paid to play the game and the player is awarded an additional 140 Otherwise, the player is awarded nothing and the casino takes the player's $4. Find the expected value E(x) to the player for one play of the game to player in a game of chance, then E(x) is negative. This value gives the average amount the player can expect to lose.
Moore’s portable X-ray equipment repair service shop receives an average of 6 portable X-ray sets per 8-hour day to be repaired. Moore would like to be able to tell his customers that they can expect one day service. What average repair time per set will the repair shop have to achieve to provide 1-day service on average? Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.
3. 4-5 Please solve the following with the provided information
Top Cutz International Barbershop is a popular haircutting and styling salon . Four barbers work full-time and spend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. REQUIRED (c) What is the average time spent in the shop?

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