Question: Problem 5. (part b.c.d only!) (a) Prove that if a nonnegative random variable X has the lack-of-memory property then it has an exponential distribution. The

Problem 5. (part b.c.d only!) (a) Prove that if a nonnegative random variable X has the lack-of-memory property then it has an exponential distribution. The number of years that a randomly chosen radio functions is an exponentially dis- tributed random variable, X, with parameter = 2. (b) Calculate the probability that a radio functions for at least 2 years. (c) Calculate the conditional probability that a radio functions for at least 4 years given that it has already worked for at least 2 years. (Hint: Lack-of-memory.) (d) A student buys a used radio without knowing its age. What is the probability that it will be working after an additional 2 years?

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