The joint pmf of a bivariate RV (X, Y) is given by p(x, y) = = Ska²y, x= 1,2; y = 1,2,3 otherwise where k is a constant. Find (a) the value of k, (b) the marginal PMF's of X and Y. (c) Are X and Y independent?
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- Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet). (units: mm Hg/10) (units: mm Hg/10) 6.5 5.4 4.2 3.3 2.1 y 43.6 32.3 26.2 16.2 13.9 Ex = 21.5, Ey = 132.2, Ex² = 104.35, Ey2 = 4086.34, Exy = 650.51, and r= 0.978. %3D Ex 21.5 Ey 132.2 Ex2 104.35 Ey2|4086.34 Exy 650.51 r 0.978 Use a 1% level of significance to test the claim that p > 0. (Use 2 decimal places.) critical t Verify that S. - 2.9006, a = -3.208, and b = 6.895. e Se a b Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x…B4Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ" (Υ - Y)2 Σ1(Y₁-Y)²¹ SxY √SXXSYY' where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)². R² = "XY =
- Let Y, and Y, have a bivariate normal distribution. The marginal distribution of Y, is normal with mean u, and variance o, f(y1) = 20í ,-0 < yı < ∞, V2no, Calculate the marginal distribution of f (y2).Consider the data (1,3), (2,5), (3,9.67) (a) Derive the normal equations for the best fit of the form f(x) = - - + Dx? (b) Find C, D using the normal equations derived above and given data. (c) Find a suitable Linearization for f (x) =- + Dx² (Don't find C, D)The following table indicates the ages of a sample of female employees of People Plus Pty, and the corresponding monthly income of each employee (in thousands of Rands). Age In Years (x) 404932273846 Monthly Income (R000s) (y) 434936314142 By completing the table given below, and then applying the relevant formulae, determine the linear regression function for this bivariate data set. X Y X^2 XY TOTAL If a female employee is 39 years of age, estimate her monthly income.
- assessment.casa.uh.edu/Assessment/Root/Pages/TestTaker/Quiz.aspx?id=2F507231-0111-4CFC-8C26-F38ED05C3949 f) O None of the above Review Later Question 7 If the LSRL relating the independent variable x and the dependent variable y for a given problem is ŷ = 2x + 4, then an increase of 1 unit in x is associated with an increase of how many units in y? a) 06 b) 00 d) O1 e) 04 Review LateThe following Table summarizes the main estimation results for the below model: C- Bo + B,R + Balet E.where (C) denotes total household Consumption in SL, (R) is the national Incorme, and (1) denotes the Taxes collected from the private sector. The time span goes from 1974, 1st quarter, to 2010, 4th quarter and all the variables are expressed in million Rupees. Dependent variable C Constant R. Coefficient Sd. Eror t-statisties 128 40 3.2 0.90 0.48 0.67 6.0 32 0.15 0.15 R squared Residual Std. 1.35 Deviation Given the information in above table and the null that the Given the information in above table and the null that the Taxes collected from the private sector (B2) is not equal to zero, O a. There is not enough information to test this hypothesis. O b. The test statistic can be computed and the null is rejected in favor of the alternative hypothesis with a 5% significance. O . None cof the these O d. The test statistic can be computed and the null is not rejected in favor of the…Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. %3D Everest climbers (summit 29,028 feet). (units: mm Hg/10) (units: mm Hg/10) 7.3 4.6 4.2 3.3 2.1 42.4 31.7 26.2 16.2 13.9 (a) Verify that Ex = 21.5, Ey = 130.4, Ex = 107.39, Ey = 3944.74, Exy = 648.03, andr 0.969. Σχ 21.5 %3D %3D Ey 130.4 Ex2 | 107.39 Ey2 3944.74 Exy 648.03 r0.9686 (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) t 6.79 critical t 1.6377 Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is…
- Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet). (units: mm Hg/10) (units: mm Hg/10) 3.3 x 6.7 Ly 42.2 4.9 4.2 2.1 31.7 26.2 16.2 13.9 (a) Verify that Ex = 21.2, Ey = 130.2, Ex? = 101.84, Ey? = 3927.82, Exy = 630.76, and r= 0.982. Ir = Ex 21.2 Ey 130.2 Ex2 101.84 Ey2 3927.82 Exy 630.76 r 0.982 (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) t 9.01 critical t 1.64 Conclusion O Reject the null hypothesis, there is sufficient evidence thatp >0. O Reject the null hypothesis, there is…A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e
