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Let f(x) = [ cx³y³ if 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise Find the following: (a) c such that f(x, y) is a probability density function: C (b) Expected values of X and Y: E(X) E(Y) = (c) Are X and Y independent? (enter YES or NO)

Let f(x) = [ cx³y³ if 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise Find the following: (a) c such that f(x, y) is a probability density function: C (b) Expected values of X and Y: E(X) E(Y) = (c) Are X and Y independent? (enter YES or NO)

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
Section13.1: Continuous Probability Models
Problem 16E
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Let f(x) = { cæºy³ if 0 ≤ x ≤ 1, 0≤ y ≤1 otherwise Find the following: (a) c such that f(x, y) is a probability density function: C = = (b) Expected values of X and Y: E(X) = = E(Y) (c) Are X and Y independent? (enter YES or NO)
Transcribed Image Text:Let f(x) = { cæºy³ if 0 ≤ x ≤ 1, 0≤ y ≤1 otherwise Find the following: (a) c such that f(x, y) is a probability density function: C = = (b) Expected values of X and Y: E(X) = = E(Y) (c) Are X and Y independent? (enter YES or NO)
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