The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 11 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 15 requests per hour. (Round your answers to four decimal places.)

(a)

What is the probability that no requests for assistance are in the system?

(b)

What is the average number of requests that will be waiting for service?

(c)

What is the average waiting time (in hours) before service begins?

h

(d)

What is the average time (in hours) at the reference desk (waiting time plus service time)?

  h

(e)

What is the probability that a new arrival has to wait for service?

Among the N=17 board members A=10 of them are also shareholders and the other N - A = 7 are non-shareholders. A committee of n=6 board members is going to be selected at random for a specific task. Use X to denote the number of board members who are also shareholders in the committee. Keep at least 4 decimal digits if the result has more decimal digits.

1. The probability that exactly 4 committee members are also shareholders is closest to

2. The probability that exactly 5 committee members are also shareholders is closest to

3. The probability that at least 5 committee members are also shareholders is closest to

4. The probability that at most 3 committee members are also shareholders is closest to

A wildlife biologist examines frogs for a genetic trait that may possibly be linked to industrial toxins in the environment. This trait is usually found in 1 of every 7 frogs, so the prevalence is 0.143. A sample of 85 frogs are collected and examined. (Enter all probabilities with 3 decimal points.)

The expected number of frogs in the sample with this trait is (enter with 2 decimal points) 12.15

What is the probability that this trait is in none of the sampled frogs? P(X=0) = 0.000

What is the probability that no more than 4 frogs in the sample have this trait? P(X =< 4) = 0.004

What is the probability that 7 or 8 frogs in the sample have this trait?

What is the probability that at least 7 frogs in the sample have this trait?

4.3. Referring to the previous problem, again suppose that a uniform prior is placed on the proportion π, and that from a random sample of 327 voters, 131 support the sales tax. Also suppose that the newspaper plans on taking a new survey of 20 voters. Let y∗ denote the number in this new sample who support the sales tax.

1. Find the posterior predictive probability that y∗ = 8.

2. Find the95% posterior predictive interval for y∗.Do this by finding the predictive probabilities for each of the possible values of y∗ and ordering them from largest probability to smallest. Then add the most probable values of y∗ into your probability set one at a time until the total probability exceeds 0.95 for the first time.

Hometown City USA is analyzing traffic patterns to determine whether traffic lights are necessary at tracked intersections. Each tracked intersection has a data file where each line contains the number of cars passing through that intersection on a given day. The data collected can cover any number of days; there can be any number of lines per file. Design an algorithm solution to read a given data file, calculate, and display the following:
number of days monitored at the intersection
maximum number of cars passing through the intersection on a tracked day
average cars per day passing through the intersection
Include the following requirements in your algorithm design:
Use a starting main module to create needed variables, read data from file, and display count and average of data in the file.
Use only simple data types, not arrays or lists in your algorithm.
In a single loop to read from the file, use an accumulator and counter to keep track of data read from file for calculating the average. Do not display data contained in the file; only calculate and display the number of days, highest number of cars for a day, and average number of cars per day contained in the file.
Remember to close the file when reading is complete

This homework will allow us to check for understanding and comfort with things you should know: Input/output, variables, expressions, conditionals, loops, arrays, functions, and classes.

• Language: Java
• Required parts:

1. Write a program that asks the user for a number, then asks for a second number, and finally prints if the first is smaller than the second, greater than the second, or equal to the second. (10 points)
2. Write a program that asks the user to enter a number, and then using a loop, outputs all integers, that are smaller than the entered number. (15 points)
3. Write a program that creates an array of 10 random numbers. After the array is created, a function receives the array, and returns the index of the highest element. (30 points)
4. Implement a class called Vehicle, with the following methods (45 points):
   • SetNumberOfPassengers(int)
     • Stores the argument value in an attribute
   • GetNumberOfPassengers()
     • Returns the attribute
   • SetNumberOfWheels(int)
     • Stores the argument value in an attribute
   • GetNumberOfWheels()
     • Returns the attribute

• Bonus parts:

1. Write a program that asks the user for a number, and outputs all prime numbers smaller than the number entered (15 points)
2. Implement a class called Bicycle, which (5 points):
   • Inherits from the class Vehicle you implemented in exercise 4 of the required parts above.
   • Sets the number of passengers to 1.
   • Sets the number of wheels to 1.

Design an elevator control system for an 8 floors building, draw the logic diagram, and illustrate the system with the following situations:

1. The car is on the ground floor, John Doe wants to go from ground floor to 7th floor;

2. The car is on 8th floor, John Doe wants to go from 6th floor to the ground floor;

3. The car is moving up from 4th floor to 7th floor, John Doe wants to go from 6th floor to the ground floor;

4. The car is moving down from 7th floor to 4th floor, John Doe wants to go from 6th floor to the ground floor.

Cash Markets Assignment
I am looking for 2-3 paragraphs.

Cash markets are where or how the physical commodities are bought and sold. These markets tend to be local. For example, a corn farmer in Ottumwa IA would not sell their grain to an elevator in Crookston MN. That means cash prices are local. Since prices are determined by supply and demand, cash prices are determined by local supply and demand. Explain why the cash price for corn in Crookston MN might be different than the cash price for corn in Ottumwa IA. What types of things could influence the local cash price for corn? Think about what corn can be used for.

A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium

1)What is the torsion constant of this pendulum?

2)What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium?

3)What is the angular frequency of oscillation of this torsion pendulum?

4)Which of the following would change the period of oscillation of this torsion pendulum?

A) increasing the mass

B) decreasing the initial angular displacement

C) replacing the disk with a sphere of equal mass and radius

D)hanging the pendulum in an elevator accelerating downward