Question Solved1 Answer Please help Let \( X \) be an exponential random variable with parameter \( \lambda \). Find \[ P\left(|X-E(X)| \geq 2 \sigma_{X}\right) . \] Computer Usage In a large corporate computer network, user log-ons to the system can be modeled as a Poisson process with a mean of 25 log-ons per hour. What is the probability that there are no log-ons in an interval of six minutes? b) What is the probability that the time until the next log-on is between two and three minutes? c) Determine the interval of time such that the probability that no log-on occurs in the interval is \( 0.90 \)

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Transcribed Image Text: Let \( X \) be an exponential random variable with parameter \( \lambda \). Find \[ P\left(|X-E(X)| \geq 2 \sigma_{X}\right) . \] Computer Usage In a large corporate computer network, user log-ons to the system can be modeled as a Poisson process with a mean of 25 log-ons per hour. What is the probability that there are no log-ons in an interval of six minutes? b) What is the probability that the time until the next log-on is between two and three minutes? c) Determine the interval of time such that the probability that no log-on occurs in the interval is \( 0.90 \)
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Transcribed Image Text: Let \( X \) be an exponential random variable with parameter \( \lambda \). Find \[ P\left(|X-E(X)| \geq 2 \sigma_{X}\right) . \] Computer Usage In a large corporate computer network, user log-ons to the system can be modeled as a Poisson process with a mean of 25 log-ons per hour. What is the probability that there are no log-ons in an interval of six minutes? b) What is the probability that the time until the next log-on is between two and three minutes? c) Determine the interval of time such that the probability that no log-on occurs in the interval is \( 0.90 \)
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Step1/1Answer can be solve in below imageSolution: -X is an exponential random variable with parameterlambdaChebyshev's Inequality for exponential random variable isP{|X-E(X)| >= ksigma_(x)} <= (1)/(k^(2))where k is a constantWe have to find outP{|X-E(X)| >= 2sigma_(x)}=" ? "Write down Chebyshev's Inequality here.Now Comparing above one with Chebyshe ... See the full answer