4. A real estate agent has the data on the housing prices (X₁, in millions of pesos), the number of bedrooms in the house (X₂), and the size of the house (X3, in thousands of square feet) of the 88 properties he sold. Suppose that X~N3 (μ, E), and the mean [1.5] vector and covariance matrix are μ = [1.3 2.1 4.01 and Σ = 2.1 5.0 2.3, respectively. 14.0 2.3 2.0] L2.4] Suppose that he is interested in 0.002X₂ + 0.123X3, determine the distribution of this linear combination.
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- 1) Assuming you have a data matrix X that has n rows and p variables and you know both µ and Σ. How is (X- µ)‘Σ-1(X- µ) distributed? 2) Assuming that you don’t know the values of µ and Σ. How is the statistical distance distributed as n-p gets large?A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?4) Here are data on the lengths of male and female roaches (in mm). Your job is to find out if there is adifference between male and female roaches (this should be two sided - why?).males 15.4 13.9 12.7 9.6 6.6 10.7 9.9 13.3 16.2 9.0 11.4 16.6 12.2females 16.7 16.3 12.8 16.9 15.1 12.8 18.7 18.3 8.6 13.6 15.3 16.2 13.4It's up to you to figure out what the best procedure is, what kind of hypotheses to use, which α to use,what test to use, and so on. Make sure you follow all the appropriate steps. You should probably use Ras you’ll get done much quicker. Remember to very clearly state your results in writing. Never turn in just an R printout .Hint: how do you decide which test to use? What kind of distributions do the data have?
- A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia- tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. *8.31 What are the appropriate null and alternative hypoth- eses to compare the means of the two groups?*8.32 What is the appropriate test procedure for the hy- potheses in Problem 8.31? How can we find p value? dont use excel. solve the step by stepA possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia- tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.32 What is the appropriate test procedure for the hy- potheses ? Find the p value using the F test. Solve the step by step. do nut use excellA possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia- tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.32 What is the appropriate test procedure for the hy- potheses ? Find the p value using the F test. Solve the step by step. do not use excell. JUST I WANT TO LEARN P VALUE Using the F Test . BE CAREFUL !!!!!
- 1. In a case where f'(x) is required for f(x1) when the datapoints available are x0 and x1. Which method is best used? 2. In modified Euler'a method, the predictor is computed similar with: __ 3. In order to multiply matrices, they should be __.1- The number of items produced in a factory during a week is known to be a randomvariable with mean 50● Using Markov's inequality, what can you say about the probability that this week'sproduction exceeds 75?● If the variance of one week's production is equal to 25, then using Chebyshev'sinequality, what can be said about the probability that this week's production isbetween 40 and 60?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?
- Show that if X is not a deterministic random variable, then H(X) is strictly positive. What happens to the probabilities if a random variable is non-deterministic?What should k be for the matrix given in the question to be invertible?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?