= 3. From survival analysis point of view, the competing risk analysis amounts to modeling the distribution of the time-to-event T. Let Tx be the remaing lifetime of a subject aged x. The remaining curtate lifetime K, is defined as the integer part of Tx, i.e., Kx [TX]. By this construction, for a given integer k = N, there is an equivalent event {Kx = k} = {k ≤ Tx < k+1}. Assume that T has exponential distribution with intensity λ > 0, i.e., with pdf fr(t) = λe¯t, t≥ 0. (a) Find the survival distribution P(Tx ≥ t) of the remaining lifetime Tx. (b) From the survival distribution, specify what type of random variable Tx is? (c) Find the mortality rate Ex(t) = lim P(Tx t) ho h (d) Find the probability distribution P(Kx = k) of the curtate lifetime Kx.
= 3. From survival analysis point of view, the competing risk analysis amounts to modeling the distribution of the time-to-event T. Let Tx be the remaing lifetime of a subject aged x. The remaining curtate lifetime K, is defined as the integer part of Tx, i.e., Kx [TX]. By this construction, for a given integer k = N, there is an equivalent event {Kx = k} = {k ≤ Tx < k+1}. Assume that T has exponential distribution with intensity λ > 0, i.e., with pdf fr(t) = λe¯t, t≥ 0. (a) Find the survival distribution P(Tx ≥ t) of the remaining lifetime Tx. (b) From the survival distribution, specify what type of random variable Tx is? (c) Find the mortality rate Ex(t) = lim P(Tx t) ho h (d) Find the probability distribution P(Kx = k) of the curtate lifetime Kx.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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3. From survival analysis point of view, the competing risk analysis amounts to modeling the
distribution of the time-to-event T. Let Tx be the remaing lifetime of a subject aged x. The
remaining curtate lifetime K, is defined as the integer part of Tx, i.e., Kx [TX]. By this
construction, for a given integer k = N, there is an equivalent event {Kx = k} = {k ≤ Tx < k+1}.
Assume that T has exponential distribution with intensity λ > 0, i.e., with pdf
fr(t) = λe¯t,
t≥ 0.
(a) Find the survival distribution P(Tx ≥ t) of the remaining lifetime Tx.
(b) From the survival distribution, specify what type of random variable Tx is?
(c) Find the mortality rate
Ex(t) = lim
P(Tx <t+h|Tx > t)
ho
h
(d) Find the probability distribution P(Kx = k) of the curtate lifetime Kx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2Fd354c189-dd6e-42b2-846e-2746a1ab3cc0%2Fndx0n6_processed.png&w=3840&q=75)
Transcribed Image Text:=
3. From survival analysis point of view, the competing risk analysis amounts to modeling the
distribution of the time-to-event T. Let Tx be the remaing lifetime of a subject aged x. The
remaining curtate lifetime K, is defined as the integer part of Tx, i.e., Kx [TX]. By this
construction, for a given integer k = N, there is an equivalent event {Kx = k} = {k ≤ Tx < k+1}.
Assume that T has exponential distribution with intensity λ > 0, i.e., with pdf
fr(t) = λe¯t,
t≥ 0.
(a) Find the survival distribution P(Tx ≥ t) of the remaining lifetime Tx.
(b) From the survival distribution, specify what type of random variable Tx is?
(c) Find the mortality rate
Ex(t) = lim
P(Tx <t+h|Tx > t)
ho
h
(d) Find the probability distribution P(Kx = k) of the curtate lifetime Kx.
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