(Solved): Light bulbs of different types have a failure rate, depending on type. The lifetime of a light bulb ...

Light bulbs of different types have a failure rate, depending on type. The lifetime of a light bulb with failure rate is exponentially distributed with rate A. Assume that the failure rate of a randomly selected light bulb is uniformly distributed on (a1, a2), where 0 < a 0) unit of time, find the conditional density of the failure rate of this light bulb.