Question: A certain component is subject to electrical surges over time. Suppose that these surges occur according to a Poisson process with rate . Suppose also

A certain component is subject to electrical surges over time. Suppose that these surges occur according to a Poisson process with rate . Suppose also that with probability p, any particular surge will disable the component. What is the probability that the component survives (is not disabled) throughout the period [0, t]? [Hint: Make appropriate independence assumptions.]

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