The following figure shows probability distributions, namely, Expon1 and Expon2, of inter-arrival times forphone calls at two different call centers. Note that the inter-arrival times in each call center are exponentiallydistributed, with rates Lambda1 and Lambda2, respectively.Expon(1)Expon(2)Based on the figure, which statement is true?Lambda 1 > Lambda 2O Lambda 2> Lambda 1O Lambda 1= Lambda 2Not enough information

In this case, two exponential distributions are given.

Answered: The following figure shows probability…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question 10
Suppose that in a certain small town it either rains or is sunny every day. A meteorologist notes that when it is sunny in this town, it will be sunny the next day with probability 0.3. If it rains, it will be sunny the next day with probability 0.4. Answer the following questions:
If A, u are the rates of arrival and departure in an M/M/1 queue respectively, give the formula for the probability that there are n customers in the queue at any time in the steady-state.
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lq, Wq, c and utilization ratio.
Question 2) Waiting Line Analysis A customer service desk with 1 worker is able to process an average of 9 customer inquiries per hour. An average of 6 customers arrive for help at the desk each hour. c) What is the average time required to serve a customer (in minutes)? d) What is the probability that more than 2 customers will arrive in the next hour?
Question 16 A player of a video game is confronted with a series of 3 opponents and a(n) 70% probability of defeating each opponent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends). Round your answers to 4 decimal places. (a) What is the probability that a player defeats all 3 opponents in a game? 0.3430 (b) What is the probability that a player defeats at least 2 opponents in a game? 0.7840 (C) If the game is played 2 times, what is the probability that the player defeats all 3 opponents at least once? 0.5683
Question 20. A town has a clinic where people go to donate blood. One third of the persons donating blood at each of these clinics have O+ blood. What is the probability that in a randomly chosen day, it takes six donors to find two O* donor in the 6th donor of the day? (a) 0.3292 (b) 0.0329 (c) 0.1097 (d) 0.1314
The time that it takes to service a car is an exponential random variable with rate 1.1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability thatB’s car is ready before A’s? Assume that the service times are independent, and the servicebegins upon arrival.2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has beencompletely serviced, what is the probability that B’s car is ready before 2? Detailed explanation and calculation would be much appreciated.
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lg, Wq, c and utilization ratio.
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
Suppose the weather moves between three states 1,2,3. It stays in state 1 for an exponentially distributed number of days with mean 3, then goes to state 2. It stays in state 2 for an exponentially distributed number of days with mean 4, then goes to state 3. It stays in state 3 for an exponentially distributed number of days with mean 1, then goes to state 1. Compute the long-term probability that the weather is in state 1. Write your answer as a decimal.

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