1. If y=(₁,₂,₂) be a random vector with mean vector and covariance matrix (11 0 = 1 2 3 0 3 10 Apply the appropriate matrices and linear algebra concepts to determine parameters of the distribution for (a) z when z=2y₁-3y₂ +₁. (b) z=(2₁.2₂) with 2₁ = ₁ + ₂ + ₁ and Z₂ = 3Y₁ + Y₂ −2y₁.
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 11. 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 __.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 step
- 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.*8.32 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 !!!!!Consider a dynamic system with three states, s_1s1, s_2s2, and s_3s3. Let A = \begin{pmatrix} 0.7&0.3 &0.3 \\0.2& 0.6 & 0.2 \\ 0.1 & 0.1 &0.5 \end{pmatrix}A=⎝⎛0.70.20.10.30.60.10.30.20.5⎠⎞ be the transition matrix such that a_{ij}aij is the probability of moving from s_jsj to s_isi. Let \overrightarrow{x} = \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}x=⎝⎛x1x2x3⎠⎞ be a stationery distribution of AA with sum of elements x_1+x_2+x_3=120x1+x2+x3=120. Find x_2x2.
- 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?Find the value(s) of λ for the matrix D to be singular. D=(1,2,0 0,λ + 1,2 0,1,λ)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 population with two age classes has a Leslie matrix L . If the initial population vector x0, compute x1, x2, and x3compute e^At and e^-At of an identical matrix,I (1 0 0 1)Suppose in a scatterplot matrix, you observe that all of the scatterplots associated with the explanatory variables show a strong linear relationship. There are three explanatory variables in the model. Of the following, which is the most valid to do? Remove the response variable. Remove only one of the explanatory variables and keep only two. Remove all of the explanatory variables because they are linearly related to each other and therefore explain the same thing. Remove exactly two of the explanatory variables because they are all linearly related to each other and therefore explain the same thing. We only need to keep one in the model.