Problem 5 Let X₁,..., X₁ be a sequence of independent, identical distributed random variables, with expected value and variance o². Justifying each step, determine the following limit: lim P(X1 + X₂ + + X₂
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Q: What is the correlation coefficient? Multiple Choice −0.128 0.016 0.651 −0.053
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- Problem#1: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for(a) 1 hour(b) 15 minutes(c) 8 hoursQuestion 13 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 technical errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.Question 15 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 human errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.
- Question 10 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 0 technical errors given 3 human errors? State your answer as a decimal value rounded to two digits after the decimal point.a man is investigating the populaion of bear in two areas. Area 1 and Area 2. He expect the number of bear to be X and Y in area 1 and area 2 to be Poisson- distributeted. He expect the number og bear to be λ1 = 3 in area 1 and λ2 = 5 in area 2. Find P(X = 2) and P(X ≥3) and find an approximate value expression for P(X = Y)Question 4a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:• the type of distribution this variable has; and• the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error.iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%. iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the…
- Problem 3. Suppose a test for detecting a certain rare disease has been perfected that is capable of discovering the disease in 97% of all afflicted individuals. Suppose further that when it is tried on healthy individuals, 5% of them are incorrectly diagnosed as having the disease. Finally, suppose that when it is tried on individuals who have certain other milder diseases, 10% of them are incorrectly diagnosed. It is known that the percentages of individuals of the three types being considered here in the populations at large are 1%, 96%, and 3%, respectively. Calculate the probability that an individual, selected at random from the population at large and tested for the rare disease, actually has the disease if the test indicates he is so afflicted.Problem 1: A report states that on average Moroccan boys (12-18 years old) get a haircut 5.8 times a year. An independent researcher randomly selected 20 boys (12-18 years old) and obtained these data. 3 2 1 3 7 2 9 4 6 6 8 0 5 6 4 2 1 3 4 1 At α = 0.05, can it be concluded that the average is more than 5.8 visits per year? (Hint: use the t test)Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
- Problem 1: Suppose that amount of (8-ounce size) servings of water Americans drink daily on average is 4.6 with standard deviation of 1.4 servings and that population is assumed to be normally distributed. a) If two Americans are chosen at random from the population, find the probability that both of these Americans selected amount of daily servings (8-ounce) of water will be less than 3 servings.Answer must contain the following as shown in class examples:Denote Full graphical representation as complete as shown in applicable class example(s) full calculator syntax and also include any additional math (if needed) before including the answer rounded to nearest thousandth. b) If three Americans are chosen at random from the population, find the probability that their mean amount of daily servings of water will be less than 3 servings.Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?