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 ?

Math   Statistics-And-Probability   
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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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