A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y) is given below. Complete parts (a) through (d) below. 17 1 + 0≤x,y≤ 1, f(x,y) = 6 6 elsewhere
A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y) is given below. Complete parts (a) through (d) below. 17 1 + 0≤x,y≤ 1, f(x,y) = 6 6 elsewhere
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 21CR
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Just need help with parts b - d
(b) It is of interest to know something about the proportion of Z=X+Y, the sum of the two proportions. Find E(X+Y). Also find E(XY).
(c) Find Var(X), Var(Y), Cov(X,Y),
(d) Find Var(X+Y).
![A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for
(X,Y) is given below. Complete parts (a) through (d) below.
17
1
+
0≤x,y≤ 1,
f(x,y) =
6
6
elsewhere](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F671be518-f9e6-4df9-9304-33791fefeccb%2Fb994a41c-b42a-493d-9fa8-ebe0843fb02f%2Ftrle3l_processed.png&w=3840&q=75)
Transcribed Image Text:A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for
(X,Y) is given below. Complete parts (a) through (d) below.
17
1
+
0≤x,y≤ 1,
f(x,y) =
6
6
elsewhere
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