C#

To write a program using a stack and a program using a queue.

Code a class encapsulating a queue of foods using a circular array. A food has the following attributes: name, the number of calories per serving and the number of servings per container. Limit your queue to 20 food items. In addition to writing the enqueue, dequeue, and peek methods, you will write two more methods: a method that returns the average calories per serving of all the foods in the queue; a method that returns the food items with the highest total calories (ie: number of calories per serving * servings per container). Write a program to test your queue with all these methods

A car insurance officer can handle up to 2 claims each working day without significant delays. The average number of claims per working day is 1.7. Assume the number of claims can be modeled by a Poisson distribution.

1. What is the probability that the insurance officer will have exactly 3 claims in a day.

2. What is the probability that the insurance officer will have fewer than 44 claims in a month? Assume the month has 22 working days.  

c. Find the mean and standard deviation for the number of claims per working day.

1. Roll two dice 48 times and record the sum of the spots on the top faces as you roll. Then construct a probability distribution for your 48 sums. Using the probability distribution, you constructed, find the mean number of spots. (If you don't have two dice, then cut out 6 pieces of paper with each being the same size and with #1,2,3,4,5,6 written on them. Place the pieces of paper in a hat or bowl. Pull out a number, then replace, pull out a number again and record the sum of the 2 numbers.)

An online test allows a maximum of 10 attempts. Abdulllah will attempt the test until he
passes it. In each attempt his chance of passing the test is 40%. Find the following:

a) What is the probability that he is able to pass the test?
b) What is the expected number of attempts to pass the test?
c) What is the variance of number of attempts?
d) Given that he passed the test, what is the probability that he passed in less than 5 attempts?
e) Given that he passed the test, what is the expected number of attempts?

An insurance company is considering offering fire insurance to customers in a certain state. After examining thousands of records of insurance claims in the area, they have come up with the following information:

First convert the table into a probability distribution by dividing each number in the "Claims" column by the total number of claims. Take probability calculations to 3 decimal places.

Now, let X be the expected payout. Find E(X), the expected value of X, to two decimal places.

55. Best Electronics Inc. offers a “no hassle” returns policy. The daily number of customers
returning items follows the normal distribution. The mean number of customers returning
items is 10.3 per day and the standard deviation is 2.25 per day.
a. For any day, what is the probability that eight or fewer customers returned items?
b. For any day, what is the probability that the number of customers returning items is
between 12 and 14?
c. Is there any chance of a day with no customer returns?

I need helping showing this and computing this in excel

Suppose you flip a biased coin (that lands heads with probability p) until 2 heads appear. Let X be the number of flips needed for this two happen. Let Y be the number of flips needed for the first head to appear. Find a general expression for the condition probability mass function pY |X(i|n) when n ≥ 2. Interpret your answer, i.e., if the number of flips required for 2 heads to appear is n, what can you say about the arrival of the first head?

1. What are the three main ways of assigning a probability?

2. List four possible outcomes needed to determine probabilities?

3. An experiment consists of three stages. There are three possible outcomes in the first stage, four possible outcomes in the second stage, and two possible outcomes in the third stage. What is the total number of outcomes?

4. A box has 12 balls. If 3 balls are randomly selected with replacement from the box, how many possible samples are there?

5. 3 students will be selected from a tutorial class of 25 students for lucky prize. First student will get $50, second student $30 and third gets $10, how many possible outcomes are there?

6. A box has 20 balls. If 5 balls are randomly selected without replacement from the box, how many possible samples are there?

7. What are 4 types of probabilities?

8. The probability that price of a Economics text book (A) will increase over next semester is 0.5 while probability that the price of an Accounting text book (B) will rise over the same period is 0.7. The probability that price of both text books will rise is 0.4.

Follow the 3 steps to get the answers of the following questions:

a) What is the probability that the price of the Economics text book will not rise over the next semester?

b) What is the probability that neither book price will rise?

c) Given that the price of the Accounting text book does not rise, what is the probability that the price of the Economics text book will rise?

d) Give your opinion and justify the answer that whether price rises for two text books are mutually exclusive or not?

9. Differentiate between Discrete Random Variable and Continuous Random Variable?

10. Classify the following in either Discrete Random Variable or Continuous Random Variable and state the reason for your answer:

1. X = the number of students attending lab on Monday

2. X = the number of teachers in Oxford

3. X = the weight of a new born baby

4. X = the average number of students passed their Mid term test in a random sample of 10 tutorial classes

11. What is the probability distribution of a random variable when the coin is tossed twice describing the number of heads that turn up? Show all the steps.

12. What are the four conditions for Binomial Experiment?

13. According to the records, 30% of the businesses in US does sponsor in large scale. Just this morning 10 businesses sponsored.

1. What is the expected number of businesses that sponsor?

2. What is the standard deviation of the number of businesses that sponsor?

Air is contained in a piston-cylinder. Initially, the 0.35 kg of air is at 2 MPa and 350°C. The air is first expanded isothermally to 500 kPa, then compressed polytropically with a polytropic exponent of 1.25 to the initial pressure, and finally compressed at the constant pressure to the initial state. Calculate the net heat transfer during the polytropic process in kJ assuming constant specific heats at 300 K (with 3 significant figures).

10 kg of air occupying a cylinder volume of 0.28 m3 is allowed to expand isentropically
behind a piston to a pressure of 30 bar. The air is then heated at a constant volume. Finally, the
air is cooled at a constant pressure back to its initial conditions. The initial pressure is 60 bar.
Calculate the change in entropy, the net work done and the net heat flow. Sketch the cycle on
the p‐v and T‐s diagrams.