The math department has installed two new printers, A and B. In his quest to accelerate global warming, Alex decides to kill trees by printing textbooks. He chooses to print from printer A with probability 3/4 and from printer B with probability 1/4. While printing, printer A has probability 1/10 of jamming and immediately destroying the current sheet of paper, and printer B has an independent 1/20 chance of doing the same. Satisfied with this plan, Anton sends off his favorite linear algebra textbook for printing. After some time, the printer jams. Undeterred, Anton fixes the jam and resumes the print job. If a second jam occurs, he concludes that today is not the day, and gives up printing. Let X be a random variable denoting the number of papers used before the print job is resumed (this is sheets successfully printed plus the one destroyed), and Y be the random variable denoting the number of sheets used after the restart (successfully printed plus the one destroyed). Determine whether or not X and Y are independent.

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below:

Find the probability that she hits at most 3 red lights. Answer to 2 decimal places.

Find the probability that she hits at least 3 red lights. Answer to 2 decimal places.

How many red lights she expect to hit? Answer to 2 decimal places.

What is the standard deviation of number of red lights she hits? Answer to 3 decimal places.

Let us consider any two consecutive days. What is the chance that she hits exactly two red lights on both days? Answer to 4 decimal places.

It is estimated that an average of 30 customers will arrive at an Airport check-in counters per hour.

a) Let X be the number of customers arrive at the counter over three hours. What is the distribution of X?

b) Let X be the number of customers arrive at the counter over three hours. How many customers would you expect in three hours?

c)What is the probability of 3 customers arriving within 10 mins? State the appropriate distribution and any parameter values. Write the probability statement and show your work in order to solve the problem.

d) Let Y represent the amount of time between the 1st customer arrive and the 10th customer arrive. What is the expected value of Y?

e) If the amount of time between two customers arriving is less than a minute, the airport will open extra counters. What is the probability that the airport will open extra counters? State the appropriate distribution and any parameter values.

I need help on c, d, and e in particular. Please explain these parts in detail and show your work.

Please do these questions in Excel!

Generate a set of 1000 pairs of standard uniform random values ??and ??. Then perform the following algorithm for each of these 1000 pairs: Let the output of this algorithm be denoted by Y.

Step 1: Generate random values ?? = −?N(??) and ?? = −?N(??)

Step 2: Calculate ? = (??−?)^?/? . If ?? ≥ ?, then generate a random number ?. If ? > ?.? accept ??as ?(that is, let ? = ??); otherwise if ? ≤ ?.?, else accept −?? as ? (that is, let ? = −??). If ?? < ?, no result is obtained, and the algorithm returns to step 1. This means that the algorithm skips the pair ?? and ?? for which ?? < ? without generating any result and moves to the next pair ?? and??. After repeating the above algorithm 1000 times, a number N of the Y values will be generated. Obviously ? ≤ ?0,??? since there will be instances when a pair ?? and ?? would not generate any result, and consequently that pair would be wasted. Investigate the probability distribution of ? by doing the following:

1. Create a relative frequency histogram of ?.

2. Select a probability distribution that, in your judgement, is the best fit for ?.

3. Support your assertion above by creating a probability plot for ?.

4. Support your assertion above by performing a Chi-squared test of best fit with a 0.05 level of significance.

The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest bulk cargo port in the world. The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week (USA Today, September 25, 2012). Assume that the number of tons of cargo handled per week is normally distributed with a standard deviation of .82 million tons.

a. What is the probability that the port handles less than 5 million tons of cargo per week (to 4 decimals)?

b. What is the probability that the port handles 3 or more million tons of cargo per week (to 4 decimals)?

c. What is the probability that the port handles between 3 million and 4 million tons of cargo per week (to 4 decimals)?

d. Assume that 85% of the time the port can handle the weekly cargo volume without extending operating hours. What is the number of tons of cargo per week that will require the port to extend its operating hours (to 2 decimals)?

We are interested in studying whether education level affects people's credit default risk (failing to pay their credit debt). A random study was conducted to see the percent of those who default on their credit card was conducted.

Highest level of education attained % defaulted Number of people studied

High School    36% 100

Some College 20% 160

Bachelor's degree 15% 180

Advanced degree 6% 50

Test the null hypothesis of whether the population proportions of credit default rate is the same for all levels of education.

Provide the test statistic value from your analysis and P-value

In PYTHON 3 using functions. Per the client, you have the following information:  customer name, burger choice, time of purchase, and total bill. By the end of the day, your program will provide the following information:

1. Top three best clients with the highest spending

2. Name of client with second to last lowest bill

3. busiest hour of the day based on number of clients

Assumptions

1. Your program will not handle more than 100 clients per day

2. The restaurant only has six types of burgers

3. The restaurant works from 10:00 am until 10:00 pm

According to a report of COVID-19 death rates in the United States from CDC as of April 6th 2020, New York has around 21.2 per 100,000 people for the death rate, which is the state with the highest number of COVID-19 cases.

a) Obtain a point estimate for the population proportion of Americans who have died from COVID-19 in New York state.

b) Verify that the requirements for constructing a confidence interval about p are satisfied.

c) Construct a 90% confidence interval for the population proportion of Americans who have died in New York since the COVID-19 pandemic.

d) Interpret the interval.

Second price auction is quite similar to a first price auction(each player bids secrectly choosing a nonnegative real number) and each player i value the object v_iwhere v₁ > v₂ > ....>v_n > 0, except that the winner pays the amount of the second highest bid.

Prove that for player i, bidding v_i is a weakly dominant strategy. That is, prove that regardless of the actions of the other players, player i payoff when bidding v_i is at least as high as her payoff when making any other bid. Also, prove that there exist Nash equilibria in which player 1 does not win the auction.

Listed below are the heights of candidates who won elections and the heights of the candidates with the next highest number of votes. The data are in chronological​ order, so the corresponding heights from the two lists are matched. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a​ 95% confidence interval estimate of the mean of the population of all​ "winner/runner-up" differences. Does height appear to be an important factor in winning an​ election? Winner 71 69 71 69 70 72 73 74 ​Runner-Up 69 71 68 68 68 69 68 73