(14-i) Let Z e {0, 1,2, 3, 4}, Y € {0, 1, 2} with the joint density f(0, 0) = =f(4, 0), f(1, 1) = = f(2, 0) = f(3, 1), and f(2, 2) = . Show that the two random variables are dependent The following reasons are proposed. (a) The greatest common divisor of 1. is positive, therefore Z, Y are dependent (b) The least common multiple of +, . is positive, therefore Z, Y are dependent (c) X, Y are in fact independent. (d) P(Z = 0, Y = 1) = 0 + P(Z = 0)P(Y = 1) (e) None of the above (a) (b) (c) (d) (e) N/ (Select One)
(14-i) Let Z e {0, 1,2, 3, 4}, Y € {0, 1, 2} with the joint density f(0, 0) = =f(4, 0), f(1, 1) = = f(2, 0) = f(3, 1), and f(2, 2) = . Show that the two random variables are dependent The following reasons are proposed. (a) The greatest common divisor of 1. is positive, therefore Z, Y are dependent (b) The least common multiple of +, . is positive, therefore Z, Y are dependent (c) X, Y are in fact independent. (d) P(Z = 0, Y = 1) = 0 + P(Z = 0)P(Y = 1) (e) None of the above (a) (b) (c) (d) (e) N/ (Select One)
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...
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Transcribed Image Text:(14-i) Let Z E {0, 1, 2, 3, 4}, Y e {0, 1, 2} with the joint density f(0, 0) = = f(4, 0), f(1, 1) = = f(2, 0) = f(3, 1), and f(2, 2) = . Show that the two random variables are dependent
The following reasons are proposed.
1
1
1
(a) The greatest common divisor of
- is positive, therefore Z, Y are dependent
16 ' 4' 8
1 1
(b) The least common multiple of
16
4 ' 8
is positive, therefore Z, Y are dependent
(c) X, Y are in fact independent.
(d) P(Z = 0, Y = 1) = 0 + P(Z = 0)P(Y = 1)
(e) None of the above
(a)
(b)
(c)
(d)
(e)
N/A
(Select One)
(14-ii) For the problem (14-i) above, show that the two random variables are uncorrelated.?.
The following answers are proposed.
(a) E(ZY) = 3/2 = E(Z)E(Y). So, they are uncorrelated.
(b) E(ZY) = 3/2 and E(Z)
= 1 and E(Y) = making E(Z) + E(Y) = ; .
(c) Z and Y are, in fact, positively correlated.
(d) Since Z and Y are independent, therefore they are uncorrelated.
(e) None of the above.
(a)
(b)
(c)
(d)
(e)
N/A
(Select One)
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