Suppose the joint PMF of random variables X and Y is P(X = x, Y = y) =    3/14 , if (x, y) = (−1, 1) 2/14 , if (x, y) ∈ {(0, 1),(−1, 0),(0, 0)} 1/14 , if (x, y) ∈ {(1, 1),(1, 0),(−1, −1),(0, −1),(1, −1)} 0, otherwise (a) Find the covariance of X and Y . (b) Find the correlation of X and Y .

Suppose the joint PMF of random variables X and Y is P(X = x, Y = y) =    3/14 , if (x, y) = (−1, 1) 2/14 , if (x, y) ∈ {(0, 1),(−1, 0),(0, 0)} 1/14 , if (x, y) ∈ {(1, 1),(1, 0),(−1, −1),(0, −1),(1, −1)} 0, otherwise (a) Find the covariance of X and Y . (b) Find the correlation of X and Y .

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 44CR

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Question

Suppose the joint PMF of random variables X and Y is
P(X = x, Y = y) =



3/14 , if (x, y) = (−1, 1)
2/14 , if (x, y) ∈ {(0, 1),(−1, 0),(0, 0)}
1/14 , if (x, y) ∈ {(1, 1),(1, 0),(−1, −1),(0, −1),(1, −1)}
0, otherwise
(a) Find the covariance of X and Y .
(b) Find the correlation of X and Y .

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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