Consider a renewal process with the lifetimes X1, X2, ... having the probability density function f(x) = 0.125 (4-x) for 0 < x < 4. Determine the asymptotic expression for the probability distribution of excess life Yt: lim P(yt ≤2.75) = 0047 Determine the limiting mean excess life: lim E[t] = 0047

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 8E
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Consider a renewal process with the lifetimes X1, X2, ... having the probability density function f(x) = 0.125. (4 — x)
for 0 < x < 4.
Determine the asymptotic expression for the probability distribution of excess life Yt:
lim P(2.75) =
t→∞
Determine the limiting mean excess life:
lim E[Y] =
t→∞
=
Transcribed Image Text:Consider a renewal process with the lifetimes X1, X2, ... having the probability density function f(x) = 0.125. (4 — x) for 0 < x < 4. Determine the asymptotic expression for the probability distribution of excess life Yt: lim P(2.75) = t→∞ Determine the limiting mean excess life: lim E[Y] = t→∞ =
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