Stat 4603-5504 midterm test 统计时间序列代考 1. Let xt = 3.5 + 1.2xt−1 − .8xt−2 + wt where wt is a white noise with variance 5.5. (a) [5 marks] Identify xt as an ARMA(p, q). (i.e. find p, q and...View details
exam统计代考 Note: During the test only the use of a sheet with formulas and a calculator areallowed. QUESTION 1 (5,0) Punctuality in meetings is a worrying
Note: During the test only the use of a sheet with formulas and a calculator areallowed.
(5,0) Punctuality in meetings is a worrying factor for many Portuguese companies. To evaluate the time of delay at the beginning of the meetings, Company AB decided to collect data on this subject in its two subsidiaries, Empresa A located in Lisbon and Empresa B located in Porto. The following results were presented by Empresa A relative to the delays (in minutes) verified in the last 58 meetings.
a) Calculate the values which are missing from the table of Empresa B and interpret the results presented in the table and in the graph.
b) Comment the accuracy of the following statements, justifying your comments.
b1) In Empresa A, the most frequent delay is 12 minutes.
b2) The mean delay is higher in Empresa A than in Empresa B.
b3) The distribution of delays presents a higher dispersion in Empresa A than in Empresa B.
QUESTION 2 exam统计代考
(4,0) Since 2002 a survey has been conducted on a sample of Portuguese households about the use of new technologies. Some of the data from this study was used to study the adherence to e-commerce. The following annual values were obtained for the percentage of households linked to internet and also for an indicator of e-commerce
(Table 1). After adjusting this data with a simple linear regression model, results of Table 2 were obtained.
a) Calculate the correlation between the two variables.
b) Draw a scatterplot with the observed data and the adjusted line found with the ordinary least squares method. Comment the quality of this adjustment.
(3,0) Consider the following events A and B independent with probabilities 0,5 e 0,2, respectively.
QUESTION 4 exam统计代考
(8,0) A shirt producing company classifies the shirts they produce into three categories according to their finishing quality: “Good”, “Sufficient” and “Not sufficient”. Each shirt has a production cost of 2.50 euros. Shirts classified in the “Not sufficient” category correspond to 20% of the total production and are offered to beneficence institutions. 60% of the total production is sold with profit; this happens with 66% of the shirts with “Sufficient” quality and with 90% of the “Good” quality shirts.
a) Calculate the probability that a random chosen shirt has “Good” finishing quality.
b) Calculate the proportion of “Good” quality shirts within those that are sold with profit.
c) Assume now that the selling price of “Sufficient” quality shirts is 7.50 euros and that each shirt with category “Good” is sold by 10 euros. Consider the random variable “profit per shirt”.
c1) Define the probability function for this random variable.
c2) Define its distribution function. Using this function, calculate the probability of the profit per shirt being higher than 5 euros.
Note: If you didn’t solve a) assume that 40% of the shirts produced by this company have “Good” finishing quality.