1. (4!) points] A light bulb produced by the General Illumination Company is known to have an exponentially distributed lifetime l". However, the company has been experiencing quality control problems. n any given day, the parameter A of the PDF of l" is actually a random variable, uniformly distributed in the interval [1, 3E]. The company assumes the parameter A in tenns of a uniform random variable with PDF f[l}=2,1515% {a} {5 points] Write down the conditional PDF frlaD'H} {b} {III} points] ctive the expectation E [FLA = 1.25]. {c} {III} points] Determine the unconditional expectation EEY]. {d} {15 points] Use Bayes' rule and derive fM-f {My}