B3. A device has two components, and the lifetimes of these components are modelled by random variables Y₁ and Y₂. The first component cannot fail before the second component fails, and the joint density of Y₁ and Y₂ is determined to be f(y₁, y2) = 2e-¹e-92 for 0 < y2 < y₁ <∞. The random variable X₁ = Y₁ - Y₂ can be interpreted as the time between failures, and X₂ = Y₁+ Y₂ as the lifetime of the device. (a) Find the joint density of X₁ and X₂. (b) Show that X₁ Exponential (1).

B3. A device has two components, and the lifetimes of these components are modelled by random variables Y₁ and Y₂. The first component cannot fail before the second component fails, and the joint density of Y₁ and Y₂ is determined to be f(y₁, y2) = 2e-¹e-92 for 0 < y2 < y₁ <∞. The random variable X₁ = Y₁ - Y₂ can be interpreted as the time between failures, and X₂ = Y₁+ Y₂ as the lifetime of the device. (a) Find the joint density of X₁ and X₂. (b) Show that X₁ Exponential (1).

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.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

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