Q161 · Practice questionTechnology-activeComplex familiar1 mark
QUESTION 161
The waiting time , in minutes, for a sensor signal has probability density function
No signal has arrived in the first five minutes. A technician chooses a total elapsed time so that
Which expression gives ? The shaded region shows the event .
(A)
(B)
(C)
(D)
WORKED SOLUTION
1 markAnswer C
ANSWER
C. minutes.
Worked solution
Integrating the density gives . For ,
Set this equal to to obtain , hence minutes.
A is the unconditional median; B confuses the mean additional wait with its median; D incorrectly adds the unconditional median without preserving the time already elapsed.
Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
Select C.
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