Suppose f(x) = 1.5x for 1 < x < 1. Determine the mean and variance of...

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Suppose f(x) = 1.5x for 1 < x < 1. Determine the mean and variance of X. Mean = i Variance = i The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential distribution with = 0.00004. Round the answers to 3 decimal places. (a) What is the probability that the laser will last at least 20457 hours? i (b) What is the probability that the laser will last at most 30608 hours? i (c) What is the probability that the laser will last between 20457 and 30608 hours? i Suppose the counts recorded by a Geiger counter follow a Poisson process with an average of two counts per minute. Round the answers to 3 decimal places. (a) What is the probability that there are no counts in a 30-second interval? i (b) What is the probability that the first count occurs in less than 9 seconds? i (c) What is the probability that the first count occurs between 1 and 2 minutes after start-up? i Assume the flaws along a magnetic tape follow a Poisson distribution with a mean of 0.5 flaw per meter. Let X denote the distance between two successive flaws. (Round your answer to 4 decimal places.) (a) What is the mean of X? (b) What is the probability that there no flaws in 10 consecutive meters of tape? (a) i (b) i Suppose f(x) = 1.5x for 1 < x < 1. Determine the mean and variance of X. Mean = i Variance = i The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential distribution with = 0.00004. Round the answers to 3 decimal places. (a) What is the probability that the laser will last at least 20457 hours? i (b) What is the probability that the laser will last at most 30608 hours? i (c) What is the probability that the laser will last between 20457 and 30608 hours? i Suppose the counts recorded by a Geiger counter follow a Poisson process with an average of two counts per minute. Round the answers to 3 decimal places. (a) What is the probability that there are no counts in a 30-second interval? i (b) What is the probability that the first count occurs in less than 9 seconds? i (c) What is the probability that the first count occurs between 1 and 2 minutes after start-up? i Assume the flaws along a magnetic tape follow a Poisson distribution with a mean of 0.5 flaw per meter. Let X denote the distance between two successive flaws. (Round your answer to 4 decimal places.) (a) What is the mean of X? (b) What is the probability that there no flaws in 10 consecutive meters of tape? (a) i (b) i