Suppose d machines are subject to failures and repairs. The failure times are exponentially distributed with...
4. Each time a machine is repaired, it remains up and working for an exponentially distributed time with rate λ. It then fails, and its failure is either of two types. If it is type 1 failure, then the time to repair the machine is exponentially distributed with mean μ1; if it is a type 1 failure, then the time to repair the machine is exponentially distributed with mean μ2. Each failure is, independently of the time it took the...
2. Let X and Y be independent, exponentially distributed random variables where X has mean 1/λ and Y has mean 1/μ. (a) What is the joint p.d.f of X and Y? (b) Set up a double integral for determining Pt <X <Y) (c) Evaluate the above integral. (d) Which of the following equations true, and which are false? {Z > t} = {X > t, Y > t} (e) Compute P[Z> t) wheret 0. (f) Compute the p.d.f. of Z.
The times between parts arrive a manufacturing station is exponentially distributed with mean of 0.5 minute. What is the value of parameter? What is the median time between the parts arrive? What is the standard deviation? What is the 80th percentile? Find the probability of that more than 1 minute elapse between part arrivals. After manufacturing, computer disks are tested for errors. Let X be the number of errors detected on a randomly chosen disk. The following table presents the...
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a Poisson process with the rate ? = 7 per hour. However, if there is a vacant seat (that is if the number of customers ongoing their services is n S 7, then the new customer begins the service. However, if n 8, the new customer leaves the system Individual service times are independent exponentially distributed with the mean t o20 minutes. 1. Describe the...