Let f(x1, x2) = 1²e¬1(xi+x2). Let Y1 = X1 + X2 and X2 = Y2. (a) Find the joint distribution of Y1 and Y2: f(y1, y2) (b) Then compute the marginal density of Y1
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- Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = 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). partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure (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, and r- 0.969. %3D %3D %3D %3D %3D Σχ Ex? Ey2 Σχy (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject the null…Aviation and high altitude physiology is a specialty in the study of medicine. Let x= partial pressure of oxygen in the alveoli when breathing naturally available air. Let y= Partial pressure when breathing pure oxygen. The (x,y) that appears corresponding to elevations from 10,000 feet to 30,000 feet and 5000 foot intervals for a random sample volunteers. Although the medical data were collected using airplanes, they apply equally to mount Everest climbers (summit 20,028 feet) x 7.5 4.7 4.2 3.3 2.1 (units: mm hg\10) y 43.8 32.3 26.2 16.2 13.9 (units: mm hg\10) Σx=21.8 Σy=132.4 Σx2=111.28 Σy2= 4103.82 Σxy=673 r=.972 use a 5% level of significance to test the claim that p>0. (Use 2 decimal places) t= critical t= Se=3.3276 a=.765 b=5.898 find the predicted pressure when breathing pure oxygen for the pressure from breathing available air is x=2.5.(use two decimal places) find a 99% confidence interval for y when x=2.5.(use 1 decimal place) lower limit= upper limit=he was a 5%…(3) Find the density of Y = X² when X ~ Binomial(4, ). The following answers are proposed: (a) P(Y = k) = ()/2*, k = 0,1, 2, 3, 4. (b) P(Y = k) = (()/2* )", k= 0,1,2,3, 4. (9) %3D %3D %3D (c) P(Y = /F) = k = 0,1, 2, 3, 4. 24 (8) (d) P(Y = k²) = k = 0, 1, 2, 3, 4. 24 (e) None of the above
- 6. Let f(x1,x2) = 1²e¬Mx1+*2), Let Y1 = X1 + X2 and X2 = Y2. (a) Find the joint distribution of Y1 and Y2: f(y1, y2) (b) Then compute the marginal density of Y1Don't hand writing solution.The number of minutes that train is early or late can be modeled by a random variable whose density is given by: g(t) = {(1/972)(81 − t^2), −9 ≤ t ≤ 9, 0 elsewhere, where negative values indicate the train arriving early and positive values indicate the train arriving late. a. Find the probability that one of the train trips will arrive more than 5 minutes early. b. Find the probability that one of the train trips will arrive between 1 and 8 minutes late. c. Without integration, give the expected number of minutes early/late. Examination of the graph and recollection of properties of integrals will allow this.
- Suppose that the joint distribution function of X and Y is given by f (x, y) =x+y If 0 < x < 1 and 0For x, y ≤ (0, ∞), let X and Y have the joint density 1 -e Y f(x, y) = Y i) Compute the marginal density of Y. ii) Compute the conditional mean and variance of X given Y = y. iii) Compute Var(X).1) Consider a continuous RV, Y, with a pdf given by f(y)=ce²¹, -∞Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON