A lightbulb is installed. With probability 1/3, it burns out immediately when it is first installed. With probability 2/3, it burns out after an amount of time that is uniformly distributed on [0,3]. The expected value of the time until the lightbulb burns out is

Answer 1

pr(burnoutduringfirst three hrs)=2/3, avg time is 1.5hrs
Pr(burnoutduringon)=2/3 * t/3 where t is time burning.

now, during the burn time of the bulbs burning, the average time is 1.5 hrs burning
expected life=2/3*1.5=1hr