In: Statistics and Probability
Question 5. Consider n components of a system having independently exponentially distributed lifetimes so that Xn ~ exp(θ)
a) For a single component, find the reliability to time t1 + t2 given that the component has already lived past time t1. Why is the constant failure rate referred to as the “memory-less” property?
b) For the series of n components, find an expression for Rs(t). What is the mean lifetime of the system?