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Data was taken on height and weight from the entire population of 700 mountain gorillas living in the Democratic Republic of Congo: ht\wt light average heavy short 170 70 30 tall 85 190 155 Let X encode the weight, taking the values of a randomly chosen gorilla: 0, 1, 2 for light, average, and heavy respectively. Likewise, let Y encode the height, taking values 0 and 1 for short and tall respectively. (a) Determine the joint pmf of X and Y and the marginal pmf's of X and of Y. (b) Are X and Y independent? (c) Find the covariance of X and Y.

Data was taken on height and weight from the entire population of 700 mountain gorillas living in the Democratic Republic of Congo: ht\wt light average heavy short 170 70 30 tall 85 190 155 Let X encode the weight, taking the values of a randomly chosen gorilla: 0, 1, 2 for light, average, and heavy respectively. Likewise, let Y encode the height, taking values 0 and 1 for short and tall respectively. (a) Determine the joint pmf of X and Y and the marginal pmf's of X and of Y. (b) Are X and Y independent? (c) Find the covariance of X and Y.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 24EQ
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Data was taken on height and weight from the entire population of 700 mountain gorillas living in the Democratic Republic of Congo: ht\wt light average heavy short 170 70 30 tall 85 190 155 Let X encode the weight, taking the values of a randomly chosen gorilla: 0, 1, 2 for light, average, and heavy respectively. Likewise, let Y encode the height, taking values 0 and 1 for short and tall respectively. (a) Determine the joint pmf of X and Y and the marginal pmf's of X and of Y. (b) Are X and Y independent? (c) Find the covariance of X and Y.
Transcribed Image Text:Data was taken on height and weight from the entire population of 700 mountain gorillas living in the Democratic Republic of Congo: ht\wt light average heavy short 170 70 30 tall 85 190 155 Let X encode the weight, taking the values of a randomly chosen gorilla: 0, 1, 2 for light, average, and heavy respectively. Likewise, let Y encode the height, taking values 0 and 1 for short and tall respectively. (a) Determine the joint pmf of X and Y and the marginal pmf's of X and of Y. (b) Are X and Y independent? (c) Find the covariance of X and Y.
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