Question: Let Xk be a sequence of IID exponential random variables with mean of 1. We wish to compute For some constant y (such that y

Let Xk be a sequence of IID exponential random variables with mean of 1. We wish to compute

For some constant y (such that y > 25).
(a) Find a bound to the probability using Markov€™s inequality.
(b) Find a bound to the probability using Chebyshev€™s inequality.
(c) Find a bound to the probability using the Chernoff bound.
(d) Find an approximation to the probability using the central limit theorem.
(e) Find the exact probability.

Pi >y| Xg>y k = 1

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