elevators in a medium size building simulation 5 elevators, 10 floors people arrive according to an exponential distribution, 1/lambda=3 min they arrive of course at the ground floor (1) and either push the up button or wait if it is already pressed. they choose there floor according to the following distribution floor 7 20% of the time (cafeteria); all other floors equi-likely. they go to an elevator on their floor according to an exponential distribution and either press the direction button they are going in or wait if it is already pressed. 1/mu-2 min elevators take 30 sec/floor when moving. they allow people on the elevator to exit on a floor before entering customers. 10 sec each

elevators in a medium size building simulation 5 elevators, 10 floors people arrive according to an exponential distribution, 1/lambda=3 min they arrive of course at the ground floor (1) and either push the up button or wait if it is already pressed. they choose there floor according to the following distribution floor 7 20% of the time (cafeteria); all other floors equi-likely. they go to an elevator on their floor according to an exponential distribution and either press the direction button they are going in or wait if it is already pressed. 1/mu-2 min elevators take 30 sec/floor when moving. they allow people on the elevator to exit on a floor before entering customers. 10 sec each

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter19: Probabilistic Dynamic Programming

Section19.4: Further Examples Of Probabilistic Dynamic Programming Formulations

Problem 7P

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EXERCISE - You go to a market to pick out some gourds to decorate your house for Halloween. The market has a special October deal where you get 3 randomly chosen gourdss for $10. Each gourd can either be an orange pumpkin, a green pumpkin or a squash. The probabilities for picking each one of them are: P(orange pumpkin) = 0.6, P(green pumpkin) = 0.3, and P(squash) = 0.1. A: What is the probability that the first gourd is an orange pumpkin, the second is a green pumpkin, and the third is a squash? B: What is the probability that you get all 3 as orange pumpkins? C: What is the probability that you get no squashes? D: What is the probability that you get at least one orange pumpkin? (ANSWERE USING PYTHON)
A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, theprincipal plays the following game: She asks the first student to open all the lockers. She then asks the secondstudent to close all the even-numbered lockers. The third student is asked to check every third locker. If it isopen, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourthlocker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continuethis game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed,the student opens it. After all the students have taken turns, some of the lockers are open and some are closed.The program below, when ran, will prompt the user to enter the number of lockers in the school. After thegame is over, the program will output the number of lockers and the lockers numbers of the lockers…
Consider the following scenario:A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, thestudent opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed, the student opens it. After all the students have taken turns, some of the lockers are open and some are closed. The program see in the photo, when ran, should ask the user to enter the number of lockers in the school. The program will output the number of lockers and the…
A child visits nearby tuck shop with 100 coins in pocket. The shop has eatables with different prices.Child randomly chooses an eatable and the sale price for that is added to the total sales. Consequentlyupon each random choice the child’s coins get consumed (decreased). The child can only choose fromeatables having price below or equal to the coins left in his pocket. The child can buy eatables until thetotal sales price equals to 100. The child should get a receipt for how many total products did he buyand what was the price for each.Write a C++ program to simulate the above mentioned scenario using do while loop. Your program shouldrandomly choose a number between 1 and the total number of coins left. The process must end whenall 100 coins get consumed. For random number generation find below sample code:
Correct answer will be upvoted else Multiple Downvoted. Computer science. player begins the game from the 1-st stage and should beat the stages in expanding request of the stage number. The player dominates the match in the wake of beating the n-th stage. There is all things considered one designated spot on each stage, and there is consistently a designated spot on the 1-st stage. Toward the start of the game, just the designated spot on the 1-st stage is initiated, and any remaining designated spots are deactivated. At the point when the player gets to the I-th stage that has a designated spot, that designated spot is initiated. For each attempt of a phase, the player can either beat the stage or bomb the stage. On the off chance that they beat the I-th stage, the player is moved to the i+1-st stage. On the off chance that they bomb the I-th stage, the player is moved to the latest designated spot they actuated, and they need to beat the stages after that designated spot once…
Consider the following scenario: A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed, the student opens it. After all the students have taken turns, some of the lockers are open and some are closed. The program below, when ran, will prompt the user to enter the number of lockers in the school. After the game is over, the program will output the number of…
Dynamic Programming: Two coins X and YFlip coin X: gain 1 point for the head, and lose 1 point for the tailFlip coin Y: gain 3 points for the head, lose 3 points for the tail. After n round, if the final score is positive, you win. Otherwise, you lose. The score does not matter. Pr(s) be the probability of winning; r is the round; s is the score.P0(s) = 1 for s >= 1; P0(s) = 0 if s <= 0. a. Explain why P1(s) = 0 when s <= -3; P1(s) = 0.5 when -2 <= s <= 1; P1(s) = 1 for s >= 2. b. Explain why you must select X if s is 2 or 3, and you must select Y if s is −2 or −1. b. Determine P2(s) for each possible value of s and explain. (each probability will be one of 0, ¼, 1/2, ¾, 1) c. Fine a recurrence relation for Pr(s) with form Pr(s) = max[(?+?)/2, (?+?)/2]. Explain. d. Use Dynamic Programming to compute probability P100(0) (win the game if it has 100 rounds).
The Monty Hall game is a statistical problem: there is a TV show (like the Monty Hall show) that allows contestants to choose between three doors, A, B, and C. Behind one of these doors is a new car (the winning door), and behind the other two are goats (the losing doors). After the contestant makes a choice, the game show host shows a goat behind one of the doors NOT chosen. The contestant is then given a choice to either switch to the other, non-opened door, or stick with their original guess. The interesting part of this “game" is the statistics involved-a person has a 1/3 chance of originally picking a winning door. The other door chosen – actually has a 2/3 chance of being a winning door. Therefore, it is in the contestant's best interest to switch doors. that which is not revealed to have a goat but also was not originally You will create a program that simulates the Monty Hall game, where the computer plays the role of the host. The program must have no outputs, but 1) Ask the…
The Monty Hall game is a statistical problem: there is a TV show (like the Monty Hall show) that allows contestants to choose between three doors, A, B, and C. Behind one of these doors is a new car (the winning door), and behind the other two are goats (the losing doors). After the contestant makes a choice, the game show host shows a goat behind one of the doors NOT chosen. The contestant is then given a choice to either switch to the other, non-opened door, or stick with their original guess. The interesting part of this “game" is the statistics involved –a person has a 1/3 chance of originally picking a winning door. The other door – that which is not revealed to have a goat but also was not originally chosen – actually has a 2/3 chance of being a winning door. Therefore, it is in the contestant's best interest to switch doors. You will create a program that simulates the Monty Hall game, where the computer plays the role of the host. The program must have no outputs, but 1) Ask…
In an astronomy board game, N planets in an imaginary universe do not follow the normal law of gravitation. All the planets are positioned in a row. The planetary system can be in a stable state only if the sum of the mass of all planets at even positions is equal to the sum of the mass of planets at the odd positions. Initially, the system is not stable, but a player can destroy one planet to make it stable. Find the planet that should be destroyed to make the system stable. If no such planet exists, then return -1. If there are multiple such planets, then destroy the planet with the smallest index and return the index of the destroyed planet. Example Let N-5 and planets = [2,4,6,3,4]. Destroying the fourth planet of mass 3 will result in planets = [2,4,6,4], and here, the sum of odd positioned planets is (2+6)=8, and the sum of even positioned planets is (4+4)=8, and both are equal now. Hence, we destroy the fourth planet. 11 MNBASK19922 13 14 15 16 17 18 20 * The function is…
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