Question: The following is a question possibly involving Exponential probability distribution, Gamma Function, and/or Gamma probability distribution: Suppose that a system contains a certain type of

The following is a question possibly involving "Exponential probability distribution", "Gamma Function", and/or "Gamma probability distribution":

Suppose that a system contains a certain type of component whose time in years to failure is given by T. The random variable T is modeled nicely by the exponential distribution with mean time to failure ,8 = 5. If 5 of these components are installed in different systems. what is the probability that at least 2 are still functioning at the end of 3 years? Please round your nal answer to 4 decimal places

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