The share price of the Peston Company can be modelled by a stochastic process with the property that the risk-neutral distribution for the share price 4 years from now has density function f(x) = { 180-x 4050 if 90 ≤ x ≤ 180 otherwise Suppose that interest is compounded continuously at nominal rate 4%. Determine the current price of a share of the Peston Company. Enter your answer correct to the nearest penny, but do not enter the pound sign. Answer:
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- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?At a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average haircut taking 19 minutes. It is assumed that because of excellent reputation, customerswere always willing to wait. Calculate the following a. Average number of customers in the shop and average numbers waiting for a hair cut b .Percentage of time arrival can walk in right without having to wait c. The percentage of customers who have to wait before getting into the barber’s chairReturns earned over a given time period are called realized returns. Historical data on realized returns is often used to estimate future results. Analysts across companies use realized stock returns to estimate the risk of a stock. Consider the case of Happy Dog Soap Inc. (HDS): Five years of realized returns for HDS are given in the following table. Remember: 1. While HDS was started 40 years ago, its common stock has been publicly traded for the past 25 years. 2. The returns on its equity are calculated as arithmetic returns. 3. The historical returns for HDS for 2014 to 2018 are: 2014 2015 2016 2017 2018 Stock return 8.75% 5.95% 10.50% 14.70% 4.55% Given the preceding data, the average realized return on HDS's stock is The preceding data series represents historical returns is of HDS's historical returns. Based on this conclusion, the standard deviation of HDS's If investors expect the average realized return from 2014 to 2018 on HDS's stock to continue into the future, its…
- Estimate f(4.02, 2.01, –2.03) assuming the following. f(4, 2, –2) = 6 %3D fx(4, 2, –2) = 2 fy(4, 2, –2) = 5 f_(4, 2, –2) = 4 f(4.02, 2.01, -2.03) -An economist wants to compare the economic growth rate (%) within 50 kilometers and 100 kilometers to cities in a country. He collected 6 cities of the country, and calculated the growth rates with 50km and 100km as shown in the following table. Choose an appropriate test to validate that regions within 100km have higher economic growth rate than the regions within 50km to cities. You can make certain assumptions, but need to write to indicate your assumption. Show calculations by hand.A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.5x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.5 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find 95% confidence intervals for β0 and β1. Round the answers to three decimal places. The 95% confidence interval for β0 is ( , ). The 95% confidence interval for β1 is ( , ).
- A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Compute the error variance estimate s2. Round the answer to three decimal places.A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40°C. Round the answers to three decimal places. The 95% prediction interval is ( , )."Space Mountain", a classic attraction at Disneyland Park, attracts many tourists to take a ride. Each ride can take tourist at a rate of 5 persons/min. The park is opened at 9:00 AM. Based on daily observations, it is found that the tourist arrival rate is 8 persons/min during 9:00 AM - 12:00 PM, 5 persons/min during 12:00 PM - 3:00 PM and 2 persons/min after 3:00 PM. Apply a D/D/1 queuing model to calculate what is the maximum number of tourists waiting in the queue? (Round to the nearest integer and fill in the blank with a number only.) Tourist # 180 D/D/1 360 Time (min) A
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