Please show the calculation process in Excel, thank you

7. With the gasoline time series data from Table 8.1, show the exponential smoothing forecasts using α=0.1.

   1. Applying the MSE measure of forecast accuracy, would you prefer a smoothing

      constant of α=0.1 or α=0.2 for the gasoline sales time series?

   2. Are the results the same if you apply MAE as the measure of accuracy?

   3. What are the results if MAPE is used?

   4. Week	Sales (1000s of gallons)
      1	17
      2	21
      3	19
      4	23
      5	18
      6	16
      7	20
      8	18
      9	22
      10	20
      11	15
      12	22

Question 5.
A nailing gun produces a short, loud sound as the tool drives in a nail. The sound has an intensity
level of 136 dB at the ear of the user (0.2 m from the tool), for a duration of 0.1 s.
(a) What is the corresponding sound intensity? (1.5 marks)
(b) The tool is a good approximation to a point source of sound. What is the rate at which it
produces sound energy? (1.5 marks)
(c) How much energy would be transported to the user’s eardrum (of area 6.0 x 10-5 m2) as the
tool drives in a nail? (1.5 marks)
(d) Explain why earplugs or earmuffs are recommended to be worn when using the tool.
(0.5 mark)

The following are the data regarding quarterly sales:

1. Find the forecast value of the sales for each quarter starting with Quarter 6, by using a 4-quarter moving average.

                  Evaluate this forecasting method using MAD.

                  Evaluate this forecasting method using MSE.

                  Evaluate this forecasting method using MAPE.

                  Evaluate this forecasting method using MPE.

2. Use exponential smoothing with a smoothing constant of 0.2 and an initial value of 500 to forecast the sales for Quarter 1.

Suppose that we have a red coin and a blue coin. The red coin has probability pR = 0.1 of landing heads, and the blue coin has probability pB = 0.2 of landing heads.

(a) Write R code to generate a sequence of coin tosses, starting with the red coin, and switching coins every time a coin lands heads.

(b) Generate 1000 such sequences, each consisting of 1000 coin tosses, and use them to construct a plot of the 2.5%, 50% and 97.5% quantiles of the proportion of red coins tossed as the number of tosses increases. (c) What is the stationary distribution of colours for this process? Comment on how this experiment relates to Birkhoff’s ergodic theorem

A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14​% ​yellow, 13​% ​red, 24​% ​blue, 20​% ​orange, and 16​% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the a=0.05 level of significance.

What is the P-value of the test? (round to three decimal places as needed)

Assume Nike is exposed to a currency portfolio weighted 50 percent in Canadian dollars and 50 percent in Mexican pesos. Nike estimates the standard deviation of quarterly percentage changes to be 4 percent for the Canadian dollar and 6 percent for the Mexican peso. Also assume that Nike estimates a correlation coefficient of 0.2 between these two currencies.
a) Calculate the portfolio’s standard deviation.
b) Assuming i) normal distribution of the quarterly percentage changes of each currency (and so the same of the portfolio as well), and ii) an expected percentage change of -1 percent for the currency portfolio, calculate the maximum one-quarter loss of the currency portfolio based on a 95 percent confidence level.

For the next three problems, consider 1.0 L of a solution which is 0.6 M HC₂H₃O₂ and 0.2 M NaC₂H₃O₂ (K_a for HC₂H₃O₂ = 1.8 x 10^-5). Assume 2 significant figures in all of the given concentrations so that you should calculate all of the following pH values to two decimal places.

1. Calculate the pH of this solution.

2. Calculate the pH after 0.10 mol of HCl has been added to the original solution. Assume no volume change on addition of HCl.

3. Calculate the pH after 0.20 mol of NaOH has been added to the original buffer solution. Assume no volume change on addition of NaOH.

6) The Crescent Street Jam (a local jazz quintet, with your Professor on Piano) has market power. Consumers in Potsdam demand tickets to each (monthly) live performance according to P=18-0.2*Q (MR=18-0.4Q). The band faces a constant Marginal Cost of MC=$0.10. Their total costs are TC=150+0.1Q

a) In this setting, how many tickets should they sell to each concert to maximize profits? At what price should those tickets be sold? What are the band’s profits? Graph this scenario.

b) What would be the band’s profits if they could use 1st Degree (Perfect) price discrimination? Graph this scenario.

c) Suppose that since the band has twice monthly performances (24 per year), they choose to use block/quantity pricing to sell “season” ticket packages to individuals. A ticket can then be used for ANY of the 24 concerts in a year. Suppose individual consumers have an annual demand for tickets represented by P=6-0.2*Q. How much should the band charge for a bundle of tickets and how many tickets should be in each bundle, again assuming that MC is constant at $0.10? Graph this scenario.

d) The bar where they band plays sells Yuengling Beer. When the band is performing each consumer’s demand for Yuengling is P=8-1.5B, where B represents the quantity of beer consumed. The bar’s marginal cost is $0.50. The bar can use two-part pricing by charging a “cover” charge. How large should the cover charge be? How much should the bar charge for each beer? Graph this scenario.

Assume that you recently graduated and you just landed a job as a financial planner with the Cleveland Clinic. Your first assignment is to invest $100,000. Because the funds are to be invested at the end of one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes.

Barney Smith Investment Advisors recently issued estimates for the state of the economy and the rate of return on each state of the economy. Alta Industries, Inc. is an electronics firm; Repo Men Inc. collects past due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions.

a. Calculate the expected rate of return on each alternative.

b. Calculate the standard deviation of returns on each alternative.

c. Calculate the coefficient of variation on each alternative.

d. Calculate the beta on each alternative.