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Given below is a bivariate distribution for the random variables a and y. f(x, y) x 0.2 70 70 0.6 50 0.2 40 60 a. Compute the expected value and the variance for æ and y. E(x) = 34 E(y) = 56 Var(æ) = 384 Var(y) = 64 b. Develop a probability distribution for æ + y (to 2 decimals). * +y f(x + y) 0.2 140 0.6 70 0.2 100 c. Using the result of part (b), compute E(x + y) and Var(x + y) . E(x + y) Var(x + y) = d. Compute the covariance and correlation x and y. If required, round your answers to two decimal places. Covariance = Correlation 20

Given below is a bivariate distribution for the random variables a and y. f(x, y) x 0.2 70 70 0.6 50 0.2 40 60 a. Compute the expected value and the variance for æ and y. E(x) = 34 E(y) = 56 Var(æ) = 384 Var(y) = 64 b. Develop a probability distribution for æ + y (to 2 decimals). * +y f(x + y) 0.2 140 0.6 70 0.2 100 c. Using the result of part (b), compute E(x + y) and Var(x + y) . E(x + y) Var(x + y) = d. Compute the covariance and correlation x and y. If required, round your answers to two decimal places. Covariance = Correlation 20

Calculus For The Life Sciences
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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Given below is a bivariate distribution for the random variables a and y. f(x, y) x 0.2 70 70 0.6 50 0.2 40 60 a. Compute the expected value and the variance for æ and y. E(x) = 34 E(y) = 56 Var(æ) = 384 Var(y) = 64 b. Develop a probability distribution for æ + y (to 2 decimals). * +y f(x + y) 0.2 140 0.6 70 0.2 100 c. Using the result of part (b), compute E(x + y) and Var(x + y) . E(x + y) Var(x + y) = d. Compute the covariance and correlation x and y. If required, round your answers to two decimal places. Covariance = Correlation 20
Transcribed Image Text:Given below is a bivariate distribution for the random variables a and y. f(x, y) x 0.2 70 70 0.6 50 0.2 40 60 a. Compute the expected value and the variance for æ and y. E(x) = 34 E(y) = 56 Var(æ) = 384 Var(y) = 64 b. Develop a probability distribution for æ + y (to 2 decimals). * +y f(x + y) 0.2 140 0.6 70 0.2 100 c. Using the result of part (b), compute E(x + y) and Var(x + y) . E(x + y) Var(x + y) = d. Compute the covariance and correlation x and y. If required, round your answers to two decimal places. Covariance = Correlation 20
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