Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter >(a) the probability that a repair time exceeds 6 hours? ☐(b) the conditional probability that a repair takes at least 9 hours, given that it takes more than 8 hours?=0.2. What is

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Answered: Suppose that the time (in hours)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The life of a certain type of device has an exponentially distributed failure with rate .008 per day. a) What is the mean time to failure? b) What is the probability that 200 days will pass before a failure is observed? c) What is the probability that 4 of the next 6 failures observed will occur after 200 days have passed? d) What is the probability that at most 3 failures will occur in 200 days?
The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential distribution with the answers to 3 decimal places. (a) What is the probability that the laser will last at least 20675 hours? (b) What is the probability that the laser will last at most 30974 hours? i (c) What is the probability that the laser will last between 20675 and 30974 hours? * = 0.00004. Round
Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.e. What is the probability that there are fewer than two customers in the bakery?
If the probability density function of X is f(x)= 2xe-x² for 0
Suppose again that the lifetime of a particular model of laptop is exponentially distributed with a mean of 4 years. Suppose you bought a laptop one year ago and like it so much that you buy a second one of the same model for a friend (spouse, sibling, etc.). a) What is the probability that your laptop outlasts the laptop you bought for your friend? b) What is the expected time until one of the laptops fails?
Suppose that the time students wait for a bus can be described by a uniform random variable X, where X is between 10 minutes and 30 minutes. (a) What is the probability, P that a student will wait between 10 and 18 minutes for the next bus? P = (b) What is the probability, P that a student will have to wait at least 18 minutes for the next bus? P =
Suppose that the test score of a student taking the final of a probability course is a random variable with mean 80. (a) Give an upper bound for the probability that a student's test score will exceed 90. P{score > 90} < (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 30. What can you say about the probability that a student will score between 70 and 90 (do not use the central limit theorem)? P{70 < score < 90} ? (c) How many students would have to take the final to ensure with a probability of at least 0.95 that the class average would be within 3 of 80 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? п —
What is the probability that the total of two randomly chosen numbers exceeds 3, where the first number is chosen from a uniform distribution between 0 and 2, and the second number is selected from an exponential distribution with a mean of 1?
An average of 1 package is sent to a server in 1 second. The server, on the other hand, prepares a document using the 5 packages received. The time between packets is modeled as an exponential random variable. Let X be a random variable expressing the time it takes the server to prepare a document. The time taken to prepare a document; a) Find the probability that it is more than 10 seconds.(with detail) b) Find the probability that it is between 5 seconds and 10 seconds. (with detail)
Suppose that historically, 36% of applicants that are offered admittance to Texas Tech actually enroll, while the others take offers somewhere else. If Texas Tech will accept 9150 this coming year, what is the probability that less than 35.0064% will actually enroll? P(p^<0.350064)=
For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish

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