a) Forecast the company's market share for the 13 quarter by exponential smoothing with w=0.3. b) Calculate the Root-Mean Square Error (RMSE) for the exponential forecast using w-0.3. c) If the RMSE for the exponential forecast using w-0.5 is 2.91 then compare which forecasts is better and why?
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- The operator of a pumping station has observed that demand for waterduring early afternoon hours has an approximately exponential distribution with mean 1000cfs (cubic feet per second).a) Find the probability that the demand will exceed 700 cfs during the early afternoonon a randomly selected day.b) What water-pumping capacity should the station maintain during early afternoons sothat the probability that demand will be below the capacity on a randomly selectedday is 0.995?c) Of the three randomly selected afternoons, what is the probability that on at least twoafternoons the demand will exceed 700 cfs? 2. Let Y1 and Y2 be random variables with joint density functionf(y1, y2) = (6/7(y^2+y1y2/2) 0 < y1 < 1, 0 < y2 < 2,0, elsewherea) Find marginal density functions. Are Y1 and Y2 independent?b) Find P(0 < Y1 < 0.3, −2 < Y2 < 1).c) Find P(0.6 < Y1 < 1|0 < Y2 < 1). 3.The joint density function of Y1 and Y2 is given byf(y1, y2) = (y1 + y2), 0 <…Assume that the time it takes for bacterial growth on a dairy product after it is taken out of fridge follows an Exponential distribution with a mean of 10 minutes. What is the probability that bacterial growth will not happen in 15 minutes if the dairy product has already been out of the fridge for 10 minutes?The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).a) Find the probability that the demand will exceed 200 cfs during the early afternoon on arandomly selected day.b) What water-pumping capacity should the station maintain during early afternoons sothat the probability that demand will exceed capacity on a randomly selected day isonly .01?
- The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). b) What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will be below the capacity on a randomly selected day is 0.995? c) Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?Suppose that the length of a phone call in minutes follows exponential distribution with parameter λ=8. If some one comes ahead of you in queue of telephone booth, then find the probability that you have to wait between 10 and 20 minutes.
- Suppose that the first Section of Applied Stat class ends at 13:20 and the second starts at 13:30 with ten minutes break. Professor, who teaches both sections, wants to go to bathroom during the break. Suppose that the time that takes for professor to go to bathroom and come back to the classroom has an exponential distribution with the mean of 6.7 minutes. Find the probability that the professor will be late for class for less than 3 minutes (round to 3 decimal places).The time between landings of planes at a local airport has an exponential distribution with a mean of one hour. What is the probability that more than three planes will land in one hour? TIP: TAKE ADVANTAGE OF THE RELATIONSHIP BETWEEN POISSON AND EXPONENTIALA microprocessor that controls the tuner in color TVs fails completely at random (that is, according to the exponential distribution). Suppose that the likelihood that a microprocessor that has survived for k years fails in year k + 1 is .0036. What is the cumulative distribution function of the time until failure of the microprocessor?
- Suppose that the length of long distance phone calls, mea- sured in minutes, is known to have an exponential distribution with the average length of a call equal to 15 minutes. Find the CDF.The random variable X is exponentially distributed, where X represents the waiting time to see a shooting star during a meteor shower. If X has an average value of 45 seconds, what are the parameters of the exponential distribution?Consider a grocery store between the hours of 6 and 8pm on a weeknight. Suppose two checkout lanes are typically open, each checkout can handle customers with any number of items, and each checkout has a dedicated employee. It has been observed that checking out takes a mean of 1.5 minutes per customer and that this is approximately normally distributed with a standard deviation of .3 minutes. The mean amount of time between customer arrivals at the checkouts is 1 minute and can be approximated by an exponential distribution. A: Model the scenario where a single queue is used to feed both checkout lanes (similar to the bank example with two tellers). What is the average flow time of a customer? B: Model the scenario where each checkout lane has its own separate queue, and assume that half of the customers go to queue 1 and the rest go to queue 2. What is the average flow time of a customer in this setup? Hint: Split the customer arrivals in half (i.e., double ??) and model just a…