(3) X and Y have the joint p.d.f: f(x,y) = { k, x + y ≤ 1; elsewhere. 0, (Hint: the region where f(x,y) #0 is a square with vertices (1,0), (0, 1), (−1,0), and (0, -1). Try to discuss |x|+|y| ≤ 1 in each quadrant and figure out why.) (a) Show that k = 1/2. (b) Find the marginal p.d.f. of X and marginal p.d.f. of Y. (c) Find the mean of X, μx and the mean of Y, µy. (d) Find the variance of X, o and the variance of Y, oz. (e) Find the covariance C[X,Y]. (f) Find the variance of X+Y, Ox+y. (g) Find the covariance C[X+Y, X-Y].
(3) X and Y have the joint p.d.f: f(x,y) = { k, x + y ≤ 1; elsewhere. 0, (Hint: the region where f(x,y) #0 is a square with vertices (1,0), (0, 1), (−1,0), and (0, -1). Try to discuss |x|+|y| ≤ 1 in each quadrant and figure out why.) (a) Show that k = 1/2. (b) Find the marginal p.d.f. of X and marginal p.d.f. of Y. (c) Find the mean of X, μx and the mean of Y, µy. (d) Find the variance of X, o and the variance of Y, oz. (e) Find the covariance C[X,Y]. (f) Find the variance of X+Y, Ox+y. (g) Find the covariance C[X+Y, X-Y].
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 10E
Related questions
Question
Please this is a practice question. Please make sure to answer all parts. Thanks
![(3)
X and Y have the joint p.d.f:
f(x, y) = {
k, x + y ≤ 1;
elsewhere.
0,
(Hint: the region where f(x, y) # 0 is a square with vertices (1,0), (0, 1), (−1,0), and (0, -1).
Try to discuss |x|+|y| ≤ 1 in each quadrant and figure out why. )
(a) Show that k = 1/2.
(b) Find the marginal p.d.f. of X and marginal p.d.f. of Y.
(c) Find the mean of X, μx and the mean of Y, µy.
(d) Find the variance of X, o and the variance of y, o.
(e) Find the covariance C[X,Y].
(f) Find the variance of X+Y, o+y.
(g) Find the covariance C[X + Y, X - Y].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2Fed567308-85c0-4207-9c38-e7c148c2fdab%2F8dj3ljbf_processed.png&w=3840&q=75)
Transcribed Image Text:(3)
X and Y have the joint p.d.f:
f(x, y) = {
k, x + y ≤ 1;
elsewhere.
0,
(Hint: the region where f(x, y) # 0 is a square with vertices (1,0), (0, 1), (−1,0), and (0, -1).
Try to discuss |x|+|y| ≤ 1 in each quadrant and figure out why. )
(a) Show that k = 1/2.
(b) Find the marginal p.d.f. of X and marginal p.d.f. of Y.
(c) Find the mean of X, μx and the mean of Y, µy.
(d) Find the variance of X, o and the variance of y, o.
(e) Find the covariance C[X,Y].
(f) Find the variance of X+Y, o+y.
(g) Find the covariance C[X + Y, X - Y].
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VIEWStep 5: Find the variance of X, and the variance of Y
VIEWStep 6: Find the covariance C[X,Y].
VIEWStep 7: Find the variance of X+Y, and find the covariance C[X + Y, X - Y]
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