In the theory of probability, the piecewise-defined function for :1: M) : {\"'e

In the theory of probability, the piecewise-defined function o, 17 Kes for < 0, for > 0 17 is called the probability density for an exponential distribution with parameter . Remember this if you ever study probability. For now, just calculate as directed. (a) Every probability density function f must satisfy 15 dc 1. Use this fact to find K in the definition above. (b) Calculate the mean of the probability distribution described above. By definition, this is the improper integral shown here: (c) Find the median of the probability distribution described above. By definition, this is the number b that satisfies Answer: b