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- The following table shows the average price of tomatoes (in dollars per pound) in certain country from 2017 to 2021 Year Price 2017 1.715 2018 0.942 2019 0.916 2020 1.181 2021 1.614 Use 2017 as the base period to compute the simple index for this time series By what percentage did the price of tomatoes increase or decrease between 2017 and 2021? Calculate an exponential smoothed series for this time series, using ? = 0.6. Forecast the price of tomatoes in 2022.A share follows a discrete-time log-normal process with initial price ?=£3000, u=0.02, and o2=0.015, where the time-step is 1 year. Find the probability that a European call on the share with strike price £3300 and expiry date 4 years will be exercised. State your answer as a decimal to three significant figures.Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 73.7 Q2 82.5 Q3 108.1 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,733 Time 65.8 If the original value of the series in a Q4 was 2,197, then what is the seasonally adjusted value?
- The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .Long-distance calling plan A offers flat-rate service at 10 cents per minute. Calling plan B charges 99 cents for every call under 20 minutes; for calls over 20 minutes, the charge is 99 cents for the first 20 minutes plus 10 cents for every additional minute. (Note that these plans measure your call duration exactly, without rounding to the next minute or even second. ) If your long-distance calls have exponential distribution with expected value τ minutes, which plan offers a lower expected cost per call?Explain the different factors that account for fluctuations in time series data
- Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. Use rounded for two decimal places values for intermediate calculations. Use minus sign for negative values.Define the term 'time series data' and continue to discuss the components of a time series.What is the probability that the time of the first event that is observed to occur in a Poisson process with rate λ per unit time, after initiation at t = 0, occurs later than time t = t0, for fixed value t0 ? Justify your answer
- Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 73.8 Q2 86.1 Q3 109.2 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,291 Time 54.9 In general, what quarter is the busiest time of the year? (please just answer 1, 2, 3, or 4)Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 72.9 Q2 84.3 Q3 108.6 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,796 Time 77.4 What is the forecast for period 51, if period 51 is a Q1? (please round your answer to 1 decimal place)The distance between two subsequent rust attacks is exponentially distributed with parameter λ (the distancebetween subsequent events in a Poisson process is exponentially distributed), and we still assumethat λ = 5 per kilometer.What is the probability that the distance between two consecutive rust attacks is between 200and 300 meters ?
