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Exponential random variables — Question 215

Original QCE Vault practice · 8 marks

Q215 · Practice questionTechnology-activeComplex unfamiliar8 marks

QUESTION 215 (8 marks)

A survival model, with t in hours, is
S(t)=P(T>t)={e−0.2t,0≤t≤3,e−0.6−0.4(t−3),t>3.S(t)=P(T>t)=\begin{cases}e^{-0.2t},&0\le t\le3,\\e^{-0.6-0.4(t-3)},&t>3.\end{cases}
Continuous survival curve changing its exponential decay rate at t=3 hours.
a)
Determine the median lifetime to four decimal places.
[3 marks]
b)
Given survival to 3 hours, find mean additional lifetime and explain why T is not a single exponential variable.
[2 marks]
c)
For 100 independent items that have each survived to 3 hours, let U‾\overline U be their mean additional lifetime. The exponential standard deviation equals its mean. Use the central limit theorem to approximate P(U‾>3)P(\overline U>3) to four decimal places.
[3 marks]
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