2. The joint PMF of a bivariate RV (X, Y) is given byp(x, y):[k(2x+y), x= 1,2; y = 1, 210,otherwisewhere 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? (d) Find theconditional PMF's Pyx (yx) and Pxy(x|y) (e) Find P(Y = 2|X = 2) and P(X= 2|Y = 2).

As per our guidelines we are supposed to answer only 3 sub-parts of any questions so i am solving…

Answered: 2. The joint PMF of a bivariate RV (X,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

3y2+6xy+4x2-2y=5 find 25 times the slope of the normal line at P(-2,1)
REGRESSION 8. For the following pairs of points, verify that the least square regression line is Y'= 1.8X -8.5. X:5,8,9,7,14 Y: 3,1,6,7,19.
y 2 4 1 ГО.1 0.157 P(X, Y) = x3 0.2 0.3 %3D 5 Lo.1 0.15] a) Evaluate the marginal distribution of X and Y. b) Find P(Y/X) and P(X/Y). c) Find P(Y=2/X=3).
Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 6 recent years are shown. The regression line equation is =y′+−45.79501.34704x. The correlation coefficient is =r0.858. Compute the standard error of the estimate rounded to at least two decimal places, if appropriate. Assume =α0.05 The standard error of the estimate should or should not be calculated. S est= Number of fires x 57 45 72 69 58 47 Number of acres burned y 30 15 62 42 19 26
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…
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).
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.
17. The equation of the regression line used in statistics is O A. x = a +by O B. y = bx +a %3D O C. y' = a + bx O D. x = ay +b
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…
4.5. After fitting the regression model, y= Bo + Bix1 + Brx2+ B3x3+€ on 15 cases, it is found that the mean square error s? =3 and 0.5 0.3 0.2 0.6 0.3 6.0 0.5 0.4 (X'X)-' = 0.2 0.5 0.2 0.7 0.6 0.4 0.7 3.0 Find a. The estimate of V (ß1). b. The estimate of Cov(ß¡, ß3). c. The estimate of Corr(ß1, ß3). d. The estimate of V (ß¡ – B3).
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

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

2. The joint PMF of a bivariate RV (X, Y) is given by p(x, y) = [k(2x+y), x= 1,2; y = 1, 2 10, 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? (d) Find the