Suppose n people have a $5 bill, and n people have a $10 bill. They line up single file one night to buy a ticket that costs $5. The agent selling tickets has no change at the beginning of the night. No one ever changes place in line. If the agent does not have change for the next customer, the ticket booth shuts down. Ignore the fact this would not happen with real human beings. Each possible ordering of the customers is equally likely. What is the probability that every customer who lined up at the beginning of the process will be able to purchase a ticket? Remember, there are 2n customers, so the answer will depend on n. Use R to simulate this scenario. Your simulation will create a randomly selected ticket line. Then you determine if everyone gets to purchase a ticket. Repeat this simulation many times. Estimate the probability everyone can purchase a ticket for cases where n= 10, n = 50, and n = 99.

Suppose n people have a $5 bill, and n people have a $10 bill. They line up single file one night to buy a ticket that costs $5. The agent selling tickets has no change at the beginning of the night. No one ever changes place in line. If the agent does not have change for the next customer, the ticket booth shuts down. Ignore the fact this would not happen with real human beings. Each possible ordering of the customers is equally likely. What is the probability that every customer who lined up at the beginning of the process will be able to purchase a ticket? Remember, there are 2n customers, so the answer will depend on n. Use R to simulate this scenario. Your simulation will create a randomly selected ticket line. Then you determine if everyone gets to purchase a ticket. Repeat this simulation many times. Estimate the probability everyone can purchase a ticket for cases where n= 10, n = 50, and n = 99.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Consider the experiment where a penny is flipped, a quarter is flipped, and a 6-sided die is rolled. Let d be the number of possible outcomes of this experiment. What is the value of d? (Give your answer as a single integer with no words.) Let E be the event that both the penny and the quarter come up Tails, and the die comes up an odd number. If p(E) = , where d is your answer above, what is the value of x? Enter your answer as a single integer with no words:
Pick one million sets of 12 uniform random numbers between 0 and 1. Sum up the 12 numbers in each set. Make a histogram with these one million sums, picking some reasonable binning. You will find that the mean is (obviously?) 12 times 0.5 = 6. Perhaps more surprising, you will find that the distribution of these sums looks very much Gaussian (a "Bell Curve"). This is an example of the "Central Limit Theorem", which says that the distribution of the sum of many random variables approaches the Gaussian distribution even when the individual variables are not gaussianly distributed. mean Superimpose on the histogram an appropriately normalized Gaussian distribution of 6 and standard deviation o = 1. (Look at the solutions from the week 5 discussion session for some help, if you need it). You will find that this Gaussian works pretty well. Not for credit but for thinking: why o = 1 in this case? (An explanation will come once the solutions are posted).
What flaws does the following logic have, if any? Every horse has the same coloration. The proof is provided through induction based on the number of horses. The foundation of the induction is straightforward: If there is only one horse, the coloration is definitely that animal's own. Assume there are n horses, numbered 1 to n. The induction hypothesis states that all of the horses are the same color—let's say black. Horse 2 is quite dark. According to the induction hypothesis, horses 2 through n are all the same colour. Horses 2 through n and m must all be the same colour as horse 2. As a result, all of the horses are the same colour.
A coin is flipped ten times, and each time it lands with the same result: either heads or tails. Can there be more than four possible outcomes with just three possible tails?
Different kinds of plants live on a planet. If the nutrient of a plant runs out (its nutrient level becomes zero), the plant wastes away. There are three kinds of radiation on the planet: alpha, delta, no radiation. The different species of plants react to radiation differently. The reaction involves a change in the nutrient level of the plant and the radiation the next day. The radiation of the next day will be alpha radiation if the sum of the demand for alpha radiation over all plants is greater than the sum of the demand for delta radiation by at least three. If the demand for delta radiation is greater by at least three than the demand for alpha radiation, the radiation will be delta. If the difference is less than three, there will be no radiation. There is no radiation the first day. Each plant has a name (string), a nutrient level (int), and a boolean that denotes whether it's alive. The plant species are wombleroot, wittentoot and woreroot. The different plant species react to…
Four different machine learning algorithms are shown in this section, which may be used for supervised learning on a given dataset. Give a description of any four variables you may use to help you choose which one to utilize to determine whether or not a tumor is malignant.
All businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs. This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds. It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars. Your Tasks: Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in which you set…
Modeling the spread of a virus like COVID-19 using recursion. Let N = total population (assumed constant, disregarding deaths, births, immigration, and emigration). S n = number who are susceptible to the disease at time n (n is in weeks). I n = number who are infected (and contagious) at time n. R n = number who are recovered (and not contagiuous) at time n. The total population is divided between these three groups: N = S n + I n + R n There are several hidden assumptions here that may or may not apply to COVID-19, such as a recovered person is assumed to not be able to get the disease a second time, at least within the time window being examined. On week 0 (the start), you assume a certain small number of people have the infection (just to get things going). Everyone else is initially susceptible, and no one is recovered. There are two constants of interest: Let period = time period that it takes for an infected person to recover (recover meaning they become not infectious to…
There are m towns in a straight line, with a road joining each pair of consecutive towns. Legends say that an ordinary person in one of these towns will become a hero by completing a sequence of n quests. The first quest will be completed in their home town, but after each quest they may complete their next quest either in the same town or after moving to a neighbouring town.For example, if n = 5 and m = 4, a resident of town 2 may become a hero as follows:• begin in town 2 for quest 1,• then move to town 3 for quest 2,• stay in town 3 for quest 3,• return to town 2 for quest 4, and• move to town 1 for quest 5.Design an algorithm which runs in O(nm) time and finds the total number of waysto complete n quests.
Let predicate P(n) be true if equation Σi=1 i(i + 1) = n(n+1)(n+2) 3 is true. Keep in mind that P(n) is either true or false. It is not a number. Show that P(1) and P(2) are true. If you cannot do that, make sure that you understand what the equation says.
the knowledge-based agent is not an arbitrary program for calculating actions. It is amenable to a description at the knowledge level, where we need specify only what the agent knows and what it goains are, in order to fix its behavior. Give an Example:
Four different machine learning algorithms are shown in this section, which may be used for supervised learning on a given dataset. Give a description of any four variables you may use to help you choose which one to utilize to determine whether or not a tumor is malignant.