Question

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 ?

Answer 1

The probability density function is

f(t) = e-t, t > 0

For an exponentially distributed function with probability density function ,

f(x)-e-M,x > 0, λ > 0

the average is given by $\frac{1}{\lambda }$

For the given problem, $\lambda = 1$

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.