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Questions › DSE › DSE 2017 › Q30
2 marks, −0.666666666666667Statistics › Random variables and standard distributions › Exponential and gamma distributionsHardabout 4 min

DSE 2017 Question 30: Random variables and standard distributions

A machine starts at time 000 and fails at a random time TTT with density f(t)=13e−t/3f(t)=\tfrac13 e^{-t/3}f(t)=31​e−t/3 for t>0t>0t>0. It is not monitored until t=2t=2t=2 (a failure before 222 is discovered at 222). The expected time of discovery of the failure is

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A machine starts at time 0 and fails at a random time T with density f(t)=1/3 e^(-t/3) for t>0. It is not monitored until t=2 (a failure before 2 is discovered at 2). The expected time of discovery of the failure is (A) 2+e⁻⁶/3 (B) 2-2e^(-2/3)+5e^(-4/3) (C) 2+3e^(-2/3) (D) 3

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Exponential and gamma distributions, part of Random variables and standard distributions in Statistics.

Waiting times, memorylessness and sums of exponentials.

TestStop has 7 past-paper questions on this subtopic.

Practise Random variables and standard distributionsMore on Exponential and gamma distributions

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Question from the DSE 2017 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.