Let T denote the lifetime of an individual having the cumulative distribution function - Exp(-+-+²). F(t) = P(T ≤ t) = 1 - exp Denote by Tx := T − x the remaining lifetime of an individual aged x > 0. The curtate lifetime Kx = [Tx] defines the integer part of T, as such that P(Kx = k) = P(k ≤ Tx < k + 1). (a) Specify the survival distribution Sx(t) := P(Tx > t) of individual aged x. (b) Determine the mortality rate of the individual by working out the limit below µx(t) := lim - P(t ≤ Tx < t + h|Tx ≥ t) ho h (c) Find the probability mass function P(Kx = k) of curtate lifetime Kx. (d) Show that the expected curtate lifetime E[K,] is given by the following formula ∞ E[K] = P(Tx ≥k). k=1

Let T denote the lifetime of an individual having the cumulative distribution function - Exp(-+-+²). F(t) = P(T ≤ t) = 1 - exp Denote by Tx := T − x the remaining lifetime of an individual aged x > 0. The curtate lifetime Kx = [Tx] defines the integer part of T, as such that P(Kx = k) = P(k ≤ Tx < k + 1). (a) Specify the survival distribution Sx(t) := P(Tx > t) of individual aged x. (b) Determine the mortality rate of the individual by working out the limit below µx(t) := lim - P(t ≤ Tx < t + h|Tx ≥ t) ho h (c) Find the probability mass function P(Kx = k) of curtate lifetime Kx. (d) Show that the expected curtate lifetime E[K,] is given by the following formula ∞ E[K] = P(Tx ≥k). k=1

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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