Question
If a room has two light bulbs with the same probability density f(t) = exp(-t) for...
If a room has two light bulbs with the same probability density f(t) = exp(-t) for failure at time t, ≥ 0.
a)How long, on the average, there will be at least 1 working bulb in the room ?
b) What is the most likely time for room to go completely dark ?
Homework Answers
Answer #1
The probability density function is 
For an exponentially distributed function with probability
density function 
,
the average is given by 
For the given problem, 
a)
Hence, the expected time before failure of both the bulbs is 1/1 = 1 unit of time
there will be at least one bulb working till 1 units of time
b)
Most likely time for the room to go dark is again, 1/1 = 1 units of time.
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