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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) 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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
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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