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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